Posted September 8, 2003

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 381
Eric Hillebrand, Economics Department, LSU

Unknown Parameter Changes in GARCH and ARMA Models

Posted October 15, 2003

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm
Padmanabhan Sundar, Mathematics Department, LSU

Stochastic Navier-Stokes

Posted November 11, 2003

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 381Stochastic Navier-Stokes II: Some Basic Estimates

Posted November 18, 2003

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 381
Vochita Mihai, Department of Mathematics, LSU
Graduate Student

The Radon-Gauss Transform

Posted March 3, 2004

Last modified March 20, 2004

Probability Seminar Questions or comments?

3:40 pm – 5:00 pm Lockett 285
K Saito, Meijo University

Levy Laplacian and its Applications

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents.

LEQSF(2002-04)-ENH-TR-13

Posted October 8, 2004

Last modified March 2, 2021

Probability Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 277
Kiseop Lee, University of Louisville

Insider's hedging in a jump diffusion model

Posted March 11, 2005

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 381
Habib Ouerdiane, University of Tunis

Solutions of stochastic heat equations of convolution type

Posted March 11, 2005

Probability Seminar Questions or comments?

11:10 am – 12:00 pm Lockett 381
Habib Ouerdiane, University of Tunis

Infinite dimensional entire functions and applications to stochastic differential equations

Posted September 8, 2005

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 381
Hui-Hsiung Kuo, Mathematics Department, LSU

Interacting Fock spaces associated with probability measures

Posted September 17, 2005

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 381
Jae Gil Choi , Louisiana State University, Baton Rouge (Visiting Faculty)

Generalized analytic Feynman integrals and conditional generalized analytic Feynman integrals on function space

Posted September 19, 2005

Last modified February 20, 2022

Probability Seminar Questions or comments?

4:00 pm – 5:00 pm 1030 Magnolia Wood Avenue
Si Si, Aichi Prefectural University, Japan

Some aspects of Poisson noise

Posted September 20, 2005

Last modified February 17, 2022

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 381
Jeremy Becnel, Stephen F. Austin State University

Delta Function for an Affine Subspace

Posted October 5, 2005

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 381
Jeremy Becnel, Stephen F. Austin State University

The Delta Function for an Affine Subspace II

Posted November 9, 2005

Last modified November 22, 2005

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 381
Jeremy Becnel, Stephen F. Austin State University

An Infinite Dimensional Integral Identity for the Segal-Bargmann Transform

Posted March 8, 2006

Last modified March 2, 2021

Probability Seminar Questions or comments?

4:40 pm – 5:30 pm Lockett 381
K Saito, Meijo University

Constructions of stochastic processes

Posted September 26, 2006

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 282
Habib Ouerdiane, Faculte des Sciences de Tunis, Tunis

Introduction to Brownian Functionals, and Applications to Stochastic Differential Equations

Posted October 12, 2006

Last modified October 20, 2006

Probability Seminar Questions or comments?

3:40 pm Lockett 282(Originally scheduled for Friday, October 20, 2006, 3:40 pm)

Habib Ouerdiane, University of Tunis

Infinite Dimensional Complex Analysis, Holomorphy and Application to Gaussian and non Gaussian Analysis

Posted October 31, 2006

Probability Seminar Questions or comments?

3:40 pm Lockett 282
Habib Ouerdiane, University of Tunis

Infinite Dimensional Complex Analysis, Holomorphy and Application to Gaussian and non Gaussian Analysis Part II

Posted November 6, 2006

Probability Seminar Questions or comments?

3:40 pm 282, Lockett
Suat Namli, Louisiana State University
Graduate Student

A White Noise Analysis Approach to Orthogonal Polynomials

Posted November 28, 2006

Probability Seminar Questions or comments?

3:40 pm Lockett 282
Suat Namli, Louisiana State University
Graduate Student

Orthogonal Polynomials of Exponential and Fractional Types and Beyond

Posted December 4, 2006

Probability Seminar Questions or comments?

3:40 pm Lockett 282
Hong Yin, Department of Mathematics, LSU
Graduate Student

Backward Stochastic Differential Equations

Posted March 2, 2007

Probability Seminar Questions or comments?

4:00 pm Lockett 240
Hong Yin, Department of Mathematics, LSU
Graduate Student

Backward Stochastic Differential Equations

Posted March 26, 2007

Probability Seminar Questions or comments?

4:00 pm 240 Lockett
Suat Namli, Louisiana State University
Graduate Student

Orthogonal polynomials of the exponential and fractional type

Posted March 30, 2007

Probability Seminar Questions or comments?

4:00 pm Lockett 240
Wojbor Woyczynski , Case Western Reserve University
Center for Stochastic and Chaotic Processes in Sciences and Technology

Nonlinear evolution equations driven by Levy diffusions

Abstract: Nonlinear evolution equations, such as conservation laws, KPZ Hamilton Jacobi equations develop surprising critical behavior when driven by Levy diffusions with infinitesimal generators with different asymptotic behavior of their symbols. A study of this type of formalism is motivated by physical problems related to deposition of thin semiconductor films and flows in random media.

Posted April 19, 2007

Probability Seminar Questions or comments?

4:00 pm Lockett 240
Walfredo Javier, Department of Mathematics, Southern University

Mutual information of certain multivariate distributions

Posted October 1, 2007

Probability Seminar Questions or comments?

3:40 pm Lockett 381
Ambar Sengupta, Mathematics Department, LSU

Gaussian Matrix Integrals

Posted November 12, 2007

Probability Seminar Questions or comments?

3:30 pm Lockett 381
P. Sundar, Department of Mathematics, LSU

Fractional Gaussian integrals

Posted April 7, 2008

Probability Seminar Questions or comments?

3:40 pm Lockett 381
P. Sundar, Department of Mathematics, LSU

On the Martingale Problem

Posted April 25, 2008

Probability Seminar Questions or comments?

3:40 pm Lockett 381
Julius Esunge, Department of Mathematics, LSU
Graduate Student

Anticipating Linear SDEs

Posted September 18, 2008

Last modified September 19, 2008

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 381
Hui-Hsiung Kuo, Mathematics Department, LSU

The MRM for Orthogonal Polynomials

Posted September 18, 2008

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 381
Rahul Roy, Indian Statistical Institute, Delhi

Coverage of space by random sets

Posted October 1, 2008

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 381
Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore

Unitary Independent Increment Processes and Representations of Hilbert Tensor Algebras

Posted March 30, 2009

Last modified April 13, 2009

Probability Seminar Questions or comments?

3:10 pm – 4:00 pm Lockett 301D (Conference Room)
Jeremy Becnel, Stephen F. Austin State University

Forming the Radon Transform and Support Theorem in Infinite Dimensions

Posted September 14, 2009

Probability Seminar Questions or comments?

3:40 pm – 5:30 pm Lockett 285
Fernanda Cipriano, University of Lisbon

Habib Ouerdiane, Faculte des Sciences de Tunis, Tunis

Presentations on the Bargmann-Segal Transform and the Navier-Stokes Equation

Posted September 14, 2009

Last modified September 23, 2009

Probability Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 285
Ambar Sengupta, Mathematics Department, LSU

Noise: from White to Free

Abstract: We will discuss results of Wigner and Voiculescu connecting

classical probability theory with the algebraic theory of free probability.

Applying these ideas to a classical matrix white noise process produces a free analog.

Posted October 4, 2009

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 285
Padmanabhan Sundar, Mathematics Department, LSU

On a class of stochastic partial differential equations

Posted February 8, 2010

Last modified March 16, 2010

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 285
Michael Anshelevich, Department of Mathematics, Texas A&M University

Characterizations of free Meixner distributions

The free Meixner distributions are a very simple family of measures, relatives of the semicircle law. Despite their simplicity, they have a number of characterizations. For example, their orthogonal polynomials are the only ones with a "resolvent-type" generating function, and stochastic processes with free Meixner distributions are characterized by a quadratic regression property. Many of these characterizations arise in the context of Free Probability Theory, the relevant aspects of which will be explained (and no background in which will be assumed).

Posted April 27, 2010

Last modified April 29, 2010

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 285
Eric Hillebrand, Economics Department, LSU

Temporal Correlation of Defaults in Subprime Securitization

Posted September 22, 2010

Last modified September 24, 2010

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm 241 Lockett
Benedykt Szozda, Department of Mathematics, LSU

New approach to stochastic integration of anticipating stochastic processes

Posted November 19, 2010

Probability Seminar Questions or comments?

3:40 pm 241 Lockett
Sergey Lototsky, Department of Mathematics, University of Southern California

Wick Product in The Stochastic Burgers Equation: A Curse or a Cure?

Abstract: It has been known for a while that a nonlinear equation driven by singular noise must be interpreted in the re-normalized, or Wick, form. For the stochastic Burgers equation, Wick nonlinearity forces the solution to be a generalized process no matter how regular the random perturbation is, whence the curse. On the other hand, certain multiplicative random perturbations of the deterministic Burgers equation can only be interpreted in the Wick form, whence the cure. The analysis is based on the study of the coefficients of the chaos expansion of the solution at different stochastic scales.

Posted September 9, 2011

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm 240 Lockett
Joonhee Rhee, Soongsil University, South Korea

A Defaultable Bond Pricing under the Change of Filtration

Posted September 16, 2011

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm 240 Lockett
Joonhee Rhee, Soongsil University, South Korea

Defaultable Bond Pricing under a Change of Filtration: Part II

Posted September 24, 2011

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm 240 Lockett
Ambar Sengupta, Mathematics Department, LSU

Model-free Pricing Formulas

Posted November 7, 2011

Last modified February 20, 2022

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 240
Benedykt Szozda, Department of Mathematics, LSU

Anticipative Stochastic Integral and Near-Martingales

In this talk, we present a new approach to stochastic integration based on the concept of instantaneous independence introduced by Ayed and Kuo in 2008. We compare the new integral to well known results by Itô, Hitsuda, and Skorokhod. We also discuss some properties of the instantly independent processes, the new integral and the stochastic processes associated with the new integral. Among the properties mentioned above are the Itô formula, isometry property and a near-martingale property that arises naturally in the study of the new integral. We also present numerous examples and evaluation formulas for the new integral. This is joint work with Hui-Hsiung Kuo and Anuwat Sae-Tang.

Posted November 21, 2011

Probability Seminar Questions or comments?

3:40 pm Lockett 240
Benedykt Szozda, Department of Mathematics, LSU

Anticipative Ito formula and linear Stochastic Differential Equations with anticipating initial conditions

Abstract: In this talk we present several Ito formulas for the new stochastic integral of instantly independent and adapted processes. We give numerous examples and apply the new Ito formula to solve stochastic differential equation with anticipating initial condition. Our approach is based on results of Ayed and Kuo. This is a joint work with Hui-Hsiung Kuo and Anuwat Sae-Tang.

Posted August 5, 2012

Last modified August 21, 2012

Probability Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 240
Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore

Trotter Product Formula for Stochastic Evolutions in Fock space

Posted September 7, 2012

Probability Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 240
Habib Ouerdiane, University of Tunis El Manar

Unitarising measure for the representation of Lie group and associated invariant differential operators.

Posted October 1, 2012

Last modified October 8, 2012

Probability Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 240
Irina Craciun, Department of Mathematics, LSU
Graduate Student

Gaussian Measure for Subspaces of a Banach Space

Posted September 11, 2013

Last modified September 15, 2013

Probability Seminar Questions or comments?

3:30 pm – 5:00 pm Lockett 285
Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore

Stopping CCR-flows

Posted October 15, 2013

Last modified November 9, 2013

Probability Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 381
Jimmie Lawson, Mathematics Department, LSU

Random Variables with Values In Nonpositively Curved Metric Spaces

Posted November 13, 2013

Last modified July 26, 2015

Probability Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 381
Jimmie Lawson, Mathematics Department, LSU

Random Variables with Values In Nonpositively Curved Metric Spaces

Metric spaces of nonpositive curvature (also known as CAT-0 spaces) are metric generalizations of Riemannian manifolds and have been widely studied in recent years. We review how

significant parts of the basic theory of real random variables have have

been extended to the setting of RVs with values in such spaces. Recently

Y. Lim and the presenter have used this machinery to solve a basic open

problem about matrix means of positive definite matrices.

Posted March 31, 2014

Probability Seminar Questions or comments?

1:30 pm – 2:20 pm Lockett 112
Irina Holmes, LSU

The Gaussian Radon transform and machine learning

Abstract: In this talk we investigate possible applications of the infinite dimensional Gaussian Radon transform for Banach spaces to machine learning. Specifically, we show that the Gaussian Radon transform offers a valid stochastic interpretation to the ridge regression problem in the case when the reproducing kernel Hilbert space in question is infinite-dimensional.

Posted March 25, 2015

Last modified August 19, 2015

Probability Seminar Questions or comments?

2:30 pm – 3:20 pm Lockett 284
Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore

Brownian Bridge in Quantum Probability

Posted September 11, 2015

Probability Seminar Questions or comments?

3:30 pm – 4:30 pm 285 Lockett
Arnab Ganguly, LSU

Moderate and large deviation principles for stochastic differential equations

Abstract: Moderate and large deviation principles involve estimating the probabilities of rare events. In particular, they often help to assess the quality of approximating models obtained through law of large number-type results. The talk will first give an introduction to large deviation principles and then focus on a weak convergence based approach of proving them for stochastic differential equations.

Posted September 20, 2015

Probability Seminar Questions or comments?

3:30 pm – 4:30 pm 285 Lockett
Karl Mahlburg, Department of Mathematics, LSU

Loeb Measure and Additive Number Theory

Abstract: Additive Number Theory is concerned with questions regarding the density of various sets of integers, and how these are affected by arithmetic operations. As a notable example, Szemeredi\'s Theorem from 1975 states that any set of natural numbers with positive (upper) density contains arbitrarily long arithmetic progressions. I will discuss applications of continuous (and probabilistic) techniques in Number Theory, particularly the construction of Loeb measure on the hyperfinite integers from nonstandard analysis. Once recent result is a partial proof of a conjecture of Erdos, which states that if A has positive density, then there exist two infinite sets B and C such that B + C is contained in A; the present result shows that this is true up to at most one additional shift.

Posted September 24, 2015

Probability Seminar Questions or comments?

3:30 pm – 4:30 pm 285 Lockett
Xiaoliang Wan, Louisiana State University

Some numerical issues in applying large deviation principle

Abstract: In this talk, we mainly address two numerical issues in applying the large deviation principle to spatially extended systems. The first issue is to deal with the difficulties induced by the separation of slow and fast dynamics, where will introduce a new minimum action method. The second issue is to deal with the inverse of the spatial covariance operator. This issue will be illustrated by an elliptic problem perturbed by small spatial Gaussian noise.

Posted October 2, 2015

Probability Seminar Questions or comments?

3:30 pm – 4:30 pm 285 Lockett
P. Sundar, Department of Mathematics, LSU

The Boltzmann equation and related processes

Abstract: The Boltzmann equation will be considered in weak form, and viewed as the Kolmogorov equation for a stochastic process after a spatial smoothing is introduced. The process is identified as the solution of a McKean-Vlasov equation with jumps. Its invariant measure will be verified in the Gaussian case.

Posted October 9, 2015

Probability Seminar Questions or comments?

3:30 pm – 4:30 pm 285 Lockett
Ambar Sengupta, Mathematics Department, LSU

Gaussian Random Matrices and the Large-N Limit

Abstract: A Gaussian random matrix A is an NxN matrix whose entries are random variables with jointly Gaussian distribution. In this talk we will explore the behavior of some natural functions of such matrices, such as the traces of powers of A. We will also discuss the limiting behavior of such functions when N goes to infinity. This is an expository talk and we will use little more than basic matrix algebra and knowledge of the standard Gaussian distribution.

Posted November 13, 2015

Probability Seminar Questions or comments?

3:30 pm – 4:30 pm 285 Lockett
Supratik Mukhopadhyay, Division of Computer Science and Engineering, LSU

Synthesis of Geometry Proof Problems

We present an automated methodology for generating geometric proof problems of the kind found in a high school curriculum. We formalize the notion of a geometry proof problem and describe an algorithm for generating such problems over a user-provided figure. Our experimental results indicate that our problem generation algorithm can effectively generate proof problems in elementary geometry. On a corpus of 110 figures taken from popular geometry textbooks, our system generated an average of about 443 problems per figure in an average time of 4.7 seconds per figure. This is a joint work with S. Gulwani (Microsoft Research, Redmond) and R. Majumdar (Max Planck Institute-SWS)

Posted November 20, 2015

Probability Seminar Questions or comments?

3:30 pm – 4:30 pm 285 Lockett
Shuangqing Wei , School of Electrical Engineering and Computer Science, LSU

Transmission of Partitioning Information over Non-Adaptive Noisy Multi-Access Boolean Channel

Abstract: In this talk, we first formulate a problem on the transmission of partitioning information over noisy Boolean multi-access channels. The objective of transmission is not for message restoration purpose, but rather to make active users partitioned into distinct groups so that they can transmit their messages without collision subsequently. Under a novel framework for strong coloring of hypergraphs, we then modify the sequential decoding method used in the case without noise, and present a general decoding method based on strong typical set and joint decision approaches. A large deviation technique is then employed to find the deviation exponent for the induced Markov chain in a simple but nontrivial case with two active users. The derived achievable bound is shown better when the noise is small than the converse bound of group testing, which is intended for identification of all active users, rather than the partition we are seeking for, thereby further demonstrating the uniqueness of our problems.

Posted November 28, 2015

Last modified February 20, 2022

Probability Seminar Questions or comments?

3:30 pm – 4:30 pm 285 Lockett
Hyun Woo Jeon, Dept. of Mechanical and Industrial Engineering, LSU

Manufacturing Energy Models based on Probabilistic Approaches

Many managerial decisions impact energy consumption of discrete manufacturing firms. Since an energy amount to be consumed in manufacturing systems is closely connected to energy costs and environmental consequences, these managerial decisions can have long-lasting effects. Hence, making informed decisions with the aid of energy estimation tools is important to manufacturing firms. Estimating energy consumption in manufacturing is not, however, straightforward. There are a number of different manufacturing processes, and energy consumption of each process is dependent on many operational parameters. Thus, for better manufacturing energy analysis, power profiles need to be collected and analyzed from real manufacturing machines, and various methods including analytical and simulation approaches should be proposed and tested based on the collected data. Furthermore, since many previous studies are focusing on mean power demands for evaluating energy consumption, variability of manufacturing power demands also need to be investigated to explore how the uncertainty impacts manufacturing energy.

Addressing the issues, this study proposes methods and applications of probabilistic approaches. At the beginning, this study introduces an analytical manufacturing energy model based on queueing network theory. In the model, manufacturing energy consumption is presented in a closed form equation by considering Markovian and non-Markovian assumptions. Then, this analysis develops previous models further for energy efficiency benchmarking. Comparing manufacturing energy in a hypothetical system with that of peers in the U.S., the proposed model shows how to assess energy efficiency in a manufacturing plant based on simulation and stochastic frontier analysis. After energy estimation and energy efficiency assessment are discussed, this study transcends previous studies by considering uncertainty and variability on manufacturing electrical demands. The approach presents benefits of considering uncertainty in manufacturing power demands, and proposes a systemic method to estimate mean and uncertainty by applying probabilistic techniques. At each discussion, a proposed method is validated and verified in a suitable manner, and accuracy of the proposed method is also checked in detail.

Posted March 14, 2016

Probability Seminar Questions or comments?

3:30 pm – 4:30 pm 244 Locket
Arnab Ganguly, LSU

An introduction to large deviation principle

In this talk, I will present a weak convergence based approach to large deviation principle. This approach uses appropriate variational representations of certain functionals and has also connections to control theory. The talk will illustrate the main ideas through a proof of the classical Sanov\'s theorem.

Posted March 28, 2016

Probability Seminar Questions or comments?

3:30 pm – 4:30 pm 244 Lockett
Arnab Ganguly, LSU

An introduction to large deviation principle - Part II

This will be a continuation of my previous talk. In this talk, I will continue with a weak convergence based approach to large deviation principle. This approach uses appropriate variational representations of certain functionals and has also connections to control theory. The talk will illustrate the main ideas through a proof of the classical Sanov\'s theorem.

Posted April 11, 2016

Probability Seminar Questions or comments?

3:30 pm – 4:30 pm 244 Lockett
Hui-Hsiung Kuo, Mathematics Department, LSU

Some ideas on extending the Ito theory of stochastic integration

Posted March 8, 2017

Last modified March 13, 2017

Probability Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 237
Parisa Fatheddin, Air Force Institute of Technology

Asymptotic Behavior of a Class of SPDEs

Abstract: We consider a class of stochastic partial differential equations (SPDEs) that can be used to represent two commonly studied population models: super-Brownian motion and Fleming-Viot Process. After introducing these models, we establish their asymptotic limits by means of Large and Moderate deviations, Central Limit Theorem and Law of the Iterated Logarithm. These results were achieved by joint work with Prof. P. Sundar and Prof. Jie Xiong.

Posted March 9, 2017

Last modified March 2, 2021

Probability Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 237
Hui-Hsiung Kuo, Mathematics Department, LSU

Ito's formula for adapted and instantly independent stochastic processes

Posted February 4, 2018

Probability Seminar Questions or comments?

11:00 am – 12:00 pm Lockett 239
Irfan Alam, LSU

Introduction to nonstandard methods

Abstract: This will be an expository talk on nonstandard analysis, of potential interest to all mathematicians. The framework of nonstandard analysis can be used to make rigorous the notion of infinitesimals in Leibniz'' original Calculus. The set of real numbers is extended to a larger ordered field (containing infinite and infinitesimal elements) that preserves the logical structure of the set of real numbers in some sense. This will be made precise in the talk. The tool of nonstandard extensions is not exclusive to this setting, and this talk will highlight some of the general principles that have seen applications in probability theory, combinatorial number theory, functional analysis, mathematical physics, etc. This talk will serve as background to a subsequent talk on recent work related to Gaussian measures.

Posted February 17, 2018

Probability Seminar Questions or comments?

11:00 am – 12:00 pm Lockett 239
Irfan Alam, LSU

Introduction to nonstandard methods - Part 2

Abstract: I will continue the introduction to nonstandard methods started in the previous talk. The concept of saturation will be introduced before we generalize the theory to abstract nonstandard extensions (of arbitrary structures). Some applications to Topology and Functional Analysis will be described. I will end the talk with a description of proof methods used in my recent work on Gaussian measures.

Posted February 24, 2018

Probability Seminar Questions or comments?

11:00 am – 12:00 pm Lockett 239
Hui-Hsiung Kuo, Mathematics Department, LSU

Multiplicative renormalization method for orthogonal polynomials

Abstract: I will give a very simple talk to show how I discovered this method and how powerful it can be. The ideas will be introduced through concrete examples.

Posted March 3, 2018

Probability Seminar Questions or comments?

11:00 am – 12:00 pm Lockett 239
Irfan Alam, LSU

Introduction to nonstandard methods - Part 3

Abstract: In the first half of the talk, I will finish the basic introduction to nonstandard methods with some immediate applications to Topology and Functional Analysis (prefaced in the previous talk in this series). In the second half, I will explain my work on limits of spherical integrals and their connection with Gaussian measures from a nonstandard perspective.

Posted March 11, 2018

Probability Seminar Questions or comments?

11:00 am – 12:00 pm Lockett 239
George Cochran, Mathematics Department, LSU

Policy Iteration for Controlled Markov Chains

Abstract: In my consulting work in the gambling industry I have had several complex projects in the past five years that were solved using the algorithm of policy iteration in a controlled Markov chain (or Markov decision process). The 1960 Ph.D. thesis of Ronald Howard first described this algorithm and proved convergence. This talk will describe the algorithm and why and how it applies to the particular application of determining the optimal strategy for playing the game "Ultimate X Streak".

Posted April 6, 2018

Probability Seminar Questions or comments?

11:00 am – 12:00 pm Lockett 239Exponential inequality for exit probability

Abstract: Exponential upper bounds for exit from a ball of radius $r$ before time $T$ will be discussed for Brownian motion in finite and infinite dimensions, stochastic integrals, and solutions of certain stochastic partial differential equations. The role of large deviation principle in obtaining exponential bounds will be illustrated in the context of two-dimensional stochastic Navier-Stokes equations with additive noise.

Posted April 21, 2018

Probability Seminar Questions or comments?

11:00 am – 12:00 pm Lockett 239
Arnab Ganguly, LSU

Moderate deviation of occupation measures of diffusions.

We will discuss weak convergence method to prove moderate deviations asymptotics of occupation measures of ergodic diffusions. Some concepts related to ergodicity of Markov processes will be discussed before.

Posted February 14, 2022

Probability Seminar Questions or comments?

1:00 pm – 2:00 pm Zoom
Li Chen, LSU

Dirichlet fractional Gaussian fields on the Sierpinski gasket

In this talk, we discuss the Dirichlet fractional Gaussian fields on the Sierpinski gasket. We show that they are limits of fractional discrete Gaussian fields defined on the sequence of canonical approximating graphs. This is a joint work with Fabrice Baudoin (UConn).

Posted March 2, 2022

Last modified March 7, 2022

Probability Seminar Questions or comments?

1:00 pm – 2:00 pm Zoom
George Yin, University of Connecticut

Stochastic Kolmogorov Systems: Some Recent Progress

We present some of our recent work on stochastic Kolmogorov systems. The motivation stems from dealing with important issues of ecological and biological systems. Focusing on environmental noise, we will address such fundamental questions: what are the minimal conditions for long-term persistence of a population, or long-term coexistence of interacting species. [The talk reports some of our joint work with D.H. Nguyen, N.T. Dieu, N.H. Du, and N.N Nguyen.]

Posted February 14, 2022

Last modified April 1, 2022

Probability Seminar Questions or comments?

1:00 pm – 2:00 pm Zoom
Erkan Nane, Auburn University

Moments of fractional stochastic heat equations in a bounded domain

We consider the fractional stochastic heat type equation with nonnegative bounded initial condition, and with noise term that behaves in space like the Riesz kernel and is possibly correlated in time, in the unit open ball centered at the origin in $\mathbb{R}^d$. When the noise term is white in time, we establish a change in the growth of the solution of these equations depending on the noise level. On the other hand when the noise term behaves in time like the fractional Brownian motion with index $H\in (1/2,1)$, we also derive explicit bounds leading to a well-known intermittency property. These results are our recent joint work with Mohammud Foondun and Ngartelbaye (Serge) Guerngar.

Posted February 14, 2022

Last modified April 8, 2022

Probability Seminar Questions or comments?

1:00 pm – 2:00 pm Zoom
Le Chen, Auburn University

Exact solvability and moment asymptotics of SPDEs with time-independent noise

In this talk, I will report a joint work with Raluca Balan and Xia Chen and a following-up work with Nicholas Eisenberg. In this line of research, we first study the stochastic wave equation in dimensions $d\leq 3$, driven by a Gaussian noise $\dot{W}$ which does not depend on time. We assume that the spatial noise is either white, or the covariance functional of the noise satisfies a scaling property similar to the Riesz kernel. The solution is interpreted in the Skorohod sense using Malliavin calculus. We obtain the exact asymptotic behaviour of the $p$-th moment of the solution when either the time or $p$ goes to infinity. For the critical case, namely, when $d=3$ and the spatial noise is white, we obtain the exact transition time for the second moment to be finite. The main obstacle for this work is the lack of the Feynman-Kac representation for the moment, which has been overcome by a careful analysis of the Wiener chaos expansion. Our methods turn out to be very general and can be applied to a broad class of SPDEs, which include stochastic heat and wave equations as two special cases.

Posted February 14, 2022

Probability Seminar Questions or comments?

1:00 pm – 2:00 pm Zoom
Fabrice Baudoin, University of Connecticut

Asymptotic windings of the block determinants of a unitary Brownian motion and related diffusions

We study several matrix diffusion processes constructed from a unitary Brownian motion. In particular, we use the Stiefel fibration to lift the Brownian motion of the complex Grassmannian to the complex Stiefel manifold and deduce a skew-product decomposition of the Stiefel Brownian motion. As an application, we prove asymptotic laws for the determinants of the block entries of the unitary Brownian motion. This is a joint work with Jing Wang (Purdue University)

Posted March 2, 2022

Last modified April 19, 2022

Probability Seminar Questions or comments?

1:00 pm – 2:00 pm Zoom
Maria Gordina, University of Connecticut

Limit laws for a hypoelliptic diffusions

In this talk we will consider several classical problems for hypoelliptic diffusions: the small ball problem (SBP), Chung's laws of iterated logarithm (LIL) , and finding the Onsager-Machlup functional. Namely we will look at hypoelliptic Brownian motion on the Heisenberg group and a Kolmogorov diffusion for the SBP and LIL, and the Onsager-Machlup functional for hypoelliptic Brownian motion in the Heisenberg group. One of these processes is not Gaussian, but it has a space-time scaling property. Kolmogorov diffusion does not have this property, but it is Gaussian, so one should use a different approach. The Onsager-Machlup functional is used to describe the dynamics of a continuous stochastic process, and it is closely related to the SBP and LIL. Unlike in the Riemannian case we do not rely on the tools from differential geometry such as comparison theorems or curvature bounds as these are not easily available in the sub-Riemannian setting. The talk is based on the joint work with Marco Carfagnini.

Posted February 11, 2023

Probability Seminar Questions or comments?

12:45 pm – 2:00 pm Keisler LoungeInformal discussion on probability research topics

Posted February 11, 2023

Last modified February 24, 2023

Probability Seminar Questions or comments?

1:00 pm – 2:00 pm Lockett 135
Arnab Ganguly, LSU

Optimal learning via large deviation

Abstract: Statistical decision theory typically involves learning or estimation of a cost function from available data. The cost function in turn depends on the parameters of the underlying mathematical model of the system. We will discuss how large deviation theory can be used to develop an optimal estimator in these problems. This is a joint work with Tobias Sutter. Most of the talk should be accessible to students with only elementary knowledge of probability and statistics.

Posted March 2, 2023

Probability Seminar Questions or comments?

1:00 pm Lockett 135
Arnab Ganguly, LSU

Optimal learning via large deviation (Part II)

Statistical decision theory typically involves learning or estimation of a cost function from available data. The cost function in turn depends on the parameters of the underlying mathematical model of the system. We will discuss how large deviation theory can be used to develop an optimal estimator in these problems. This is a joint work with Tobias Sutter. Most of the talk should be accessible to students with only elementary knowledge of probability and statistics.

Posted February 11, 2023

Last modified March 20, 2023

Probability Seminar Questions or comments?

1:00 pm – 2:00 pm Zoom
Pratima Hebbar, Grinnell College

Branching Diffusion in Periodic Media

We describe the behavior of branching diffusion processes in periodic media. For a super-critical branching process, we distinguish two types of behavior for the normalized number of particles in a bounded domain, depending on the distance of the domain from the region where the bulk of the particles is located. At distances that grow linearly in time, we observe intermittency (i.e., the k-th moment dominates the k-th power of the first moment for some k), while, at distances that grow sub-linearly in time, we show that all the moments converge. A key ingredient in our analysis is a sharp estimate of the transition kernel for the branching process, valid up to linear in time distances from the location of the initial particle.

Posted March 2, 2023

Last modified March 23, 2023

Probability Seminar Questions or comments?

1:00 pm Lockett 135
Scott McKinley, Tulane University

Modeling, analysis and inference for the Generalized Langevin Equation

Fluctuating microparticles in biological fluids exhibit a wide range of anomalous behavior. From state switching (where the states cannot be directly observed) to memory effects, these particles are intrinsically Non-Markovian. In this talk, I will give a brief introduction to experimental observations that motivate using the generalized Langevin equation to model microparticle movement in mucus. In studying these paths a number of mathematical challenges arise, including determining the regularity and asymptotic behavior of these particles, and quantifying uncertainty when conducting inference.

Posted February 11, 2023

Last modified March 26, 2023

Probability Seminar Questions or comments?

1:00 pm – 2:00 pm Lockett 135
Wasiur KhudaBukhsh, University of Nottingham

Large-graph approximations for interacting particles on graphs and their applications

In this talk, we will consider stochastic processes on (random) graphs. They arise naturally in epidemiology, statistical physics, computer science and engineering disciplines. In this set-up, the vertices are endowed with a local state (e.g., immunological status in case of an epidemic process, opinion about a social situation). The local state changes dynamically as the vertex interacts with its neighbours. The interaction rules and the graph structure depend on the application-specific context. We will discuss (non-equilibrium) approximation methods for those systems as the number of vertices grow large. In particular, we will discuss three different approximations in this talk: i) approximate lumpability of Markov processes based on local symmetries (local automorphisms) of the graph, ii) functional laws of large numbers in the form of ordinary and partial differential equations, and iii) functional central limit theorems in the form of Gaussian semi-martingales. We will also briefly discuss how those approximations could be used for practical purposes, such as parameter inference from real epidemic data (e.g., COVID-19 in Ohio), designing efficient simulation algorithms etc.

Posted March 26, 2023

Last modified April 6, 2023

Probability Seminar Questions or comments?

1:00 pm Zoom (Click “Questions or Comments?” to request a Zoom link)
Samy Tindel, Purdue University

Hyperbolic Anderson model in the Skorohod and rough settings

In this talk I will start by giving a brief overview of some standard results concerning the stochastic heat equation, for which existence and uniqueness results are well established for a large class of Gaussian noises. Then I will describe some recent advances aiming at a proper definition of noisy wave equations, when specialized to a bilinear setting (called hyperbolic Anderson model). First I will focus on the so-called Skorohod setting, where an explicit chaos decomposition of the solution is available. A good control of the chaos expansion is then achieved thanks to an exponentiation trick. Next I will turn to a pathwise approach, which is based on a novel Strichartz type estimate for the wave operator. If possible I will show the main steps of this analytic estimate.

Posted February 11, 2023

Last modified April 12, 2023

Probability Seminar Questions or comments?

1:00 pm – 2:00 pm Zoom (Click “Questions or Comments?” to request a Zoom link)
Adina Oprisan, New Mexico State University

On the exit time of the Brownian motion with a power law drift

We will discuss the power law drift influence on the exit time of the Brownian motion from the half-line. The power law drift considered will emphasize the fact that the behavior of the process far away from zero will have the greatest influence. We are evaluating the time it takes for the perturbed process to hit zero using large deviations techniques. This talk is based on a joint work with D. DeBlassie and R. Smits.

Posted August 30, 2023

Probability Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232
Benjamin Fehrman, Louisiana State University

Non-equilibrium fluctuations and parabolic-hyperbolic PDE with irregular drift

Non-equilibrium behavior in physical systems is widespread. A statistical description of these events is provided by macroscopic fluctuation theory, a framework for non-equilibrium statistical mechanics that postulates a formula for the probability of a space-time fluctuation based on the constitutive equations of the system. This formula is formally obtained via a zero noise large deviations principle for the associated fluctuating hydrodynamics, which postulates a conservative, singular stochastic PDE to describe the system far-from-equilibrium. In this talk, we will focus particularly on the fluctuations of the zero range process about its hydrodynamic limit. We will show how the associated MFT and fluctuating hydrodynamics lead to a class of conservative SPDEs with irregular coefficients, and how the study of large deviations principles for the particles processes and SPDEs leads to the analysis of parabolic-hyperbolic PDEs in energy critical spaces. The analysis makes rigorous the connection between MFT and fluctuating hydrodynamics in this setting, and provides a positive answer to a long-standing open problem for the large deviations of the zero range process.

Posted September 26, 2023

Last modified October 3, 2023

Probability Seminar Questions or comments?

3:30 pm Lockett 232
Jing Wang, Purdue University

Spectral bounds for exit times of diffusions on metric measure

We consider a diffusion on a metric measure space equipped with a local regular Dirichlet form. Assuming volume doubling property and heat kernel sub-Gaussian upper bound we obtain a spectral upper bound for the survival probability $\mathbb P(\tau_D >t)$ of the diffusion, where $\tau_D$ is its first exit time from domain $D$. Among other nice consequences, we are able to obtain a uniform upper bound for the product $\lambda(D) \sup_{x\in D} \mathbb E_x(\tau_D)$. This is a joint work with Phanuel Mariano.

Posted September 25, 2023

Probability Seminar Questions or comments?

3:30 pm Lockett 232
Chuntian Wang, University of Alabama

On the impact of spatially heterogeneous human behavioral factors on 2D dynamics of infectious diseases

It is well observed that human natural and social behavior have non-negligible impacts on spread of contagious disease. For example, large scaling gathering and high level of mobility of population could lead to accelerated disease transmission, while public behavioral changes in response to pandemics may reduce infectious contacts. In order to understand spatial characteristics of epidemic outbreaks like clustering, we formulate a stochastic-statistical epidemic environment-human-interaction dynamic system, which will be called as SEEDS. In particular, a 2D agent-based biased-random-walk model with SEAIHR compartments set on a two-dimensional lattice is constructed. Two environment variables are taken into consideration to capture human natural and social behavioral factors, including population crowding effects, and public preventive measures in the presence of contagious transmissions. These two variables are assumed to guide and bias agent movement in a combined way. Numerical investigations imply that controlling mass mobility or promoting disease awareness can impede a global-scale spatial population aggregation to form, and consequently suppress disease outbreaks. Importance of coordinated public-health interventions and public compliance to these measures are explicitly demonstrated. A mechanistic interpretation of spatial geometric traits in progression of epidemic transmissions is provided through these findings, which may be useful for quantitative evaluations of a variety of public-health policies.

Posted September 25, 2023

Last modified October 26, 2023

Probability Seminar Questions or comments?

3:30 pm Zoom (Click “Questions or Comments?” to request a Zoom link)
Qi Feng, Florida State University

Entropy dissipation for general Langevin dynamics and its application

In this talk, I will discuss long-time dynamical behaviors of Langevin dynamics, including Langevin dynamics on Lie groups and mean-field underdamped Langevin dynamics. We provide unified Hessian matrix conditions for different drift and diffusion coefficients. This matrix condition is derived from the dissipation of a selected Lyapunov functional, namely the auxiliary Fisher information functional. We verify the proposed matrix conditions in various examples. I will also talk about the application in distribution sampling and optimization. This talk is based on several joint works with Erhan Bayraktar (University of Michigan) and Wuchen Li (University of South Carolina).

Posted September 28, 2023

Last modified November 3, 2023

Probability Seminar Questions or comments?

3:30 pm Lockett 232
Wasiur Khuda Bukhsh, University of Nottingham

Some approximations for stochastic epidemic models

I will talk about two approximations for stochastic compartmental models in infectious disease epidemiology. 1) Under the mass-action setup, I will discuss when one stochastic model can be approximated in some precise mathematical sense by another. In particular, I will provide error estimates in terms of a concentration inequality when an SEIR model is approximated by an SIR model. We will also consider the problem of parameter inference of such systems using notions of dynamical survival analysis (DSA). 2) The second approximation is a functional law of large numbers for an epidemic model on a configuration model random graph with interventions. No prior knowledge of epidemic models will be required.

Posted November 8, 2023

Last modified November 13, 2023

Probability Seminar Questions or comments?

3:30 pm Lockett 232
Nathan Glatt-Holtz, Tulane University

Statistical inference for high dimensional parameters from PDE constrained data: theoretical and computational developments

The Bayesian approach to inverse problems provides a principled and flexible methodology for the estimation of high dimensional unknown parameters appearing in partial differential equations. This methodology therefore represents an important frontier for statistical inference from sparse and noise corrupted data arising in physics informed settings. This talk will overview this emerging field and survey some of our recent and ongoing work in this domain. Specifically we will (i) Describe some new model PDE inference problems related to the measurement of fluid flow. (ii) Overview developments in Markov Chain Monte Carlo (MCMC) sampling methods which partially beat the curse of dimensionality and which are indispensable for resolving a wide variety of problems including the models in (i). (iii) Describe some results concerning consistency-namely the concentration of posterior measures around the true value of the unknown parameter-in the large data limit for `infinite dimensional' PDE-informed models. This is joint work with Jeff Borggaard (Virginia Tech), Christian Frederiksen (Tulane), Andrew Holbrook (UCLA), Justin Krometis (Virginia Tech), and Cecilia Mondaini (Drexel).

Posted February 21, 2024

Last modified April 8, 2024

Probability Seminar Questions or comments?

3:30 pm
Jessica Lin, McGill University

Generalized Front Propagation for Stochastic Spatial Models

In this talk, I will present a general framework which can be used to analyze the scaling limits of various stochastic spatial "population" models. Such models include ternary Branching Brownian motion subject to majority voting and several examples of interacting particle systems motivated by biology. The approach is based on moment duality and a PDE methodology introduced by Barles and Souganidis, which can be used to study the asymptotic behaviour of rescaled reaction-diffusion equations. In the limit, the models exhibit phase separation with an evolving interface which is governed by a global-in-time, generalized notion of mean-curvature flow. This talk is based on joint work with Thomas Hughes (Bath).