# Calendar

Time interval: Events:

Wednesday, September 10, 2003

Posted September 8, 2003

3:40 pm - 4:30 pm Lockett 381

Eric Hillebrand, Economics Department, LSU
Unknown Parameter Changes in GARCH and ARMA Models

Wednesday, October 22, 2003

Posted October 15, 2003

3:40 pm - 4:30 pm

Stochastic Navier-Stokes

Wednesday, November 12, 2003

Posted November 11, 2003

3:40 pm - 4:30 pm Lockett 381

Stochastic Navier-Stokes II: Some Basic Estimates

Wednesday, November 19, 2003

Posted November 18, 2003

3:40 pm - 4:30 pm Lockett 381

Vochita Mihai, Department of Mathematics, LSU Graduate Student

Monday, March 22, 2004

Posted March 3, 2004

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

Tuesday, October 12, 2004

Posted October 8, 2004

3:30 pm - 4:30 pm Lockett 277

Kiseop Lee, University of Louisville
Insider's hedging in a jump diffusion model

Thursday, March 17, 2005

Posted March 11, 2005

3:40 pm - 4:30 pm Lockett 381

Habib Ouerdiane, University of Tunis
Solutions of stochastic heat equations of convolution type

Friday, March 18, 2005

Posted March 11, 2005

11:10 am - 12:00 pm Lockett 381

Habib Ouerdiane, University of Tunis
Infinite dimensional entire functions and applications to stochastic differential equations

Wednesday, September 14, 2005

Posted September 8, 2005

3:40 pm - 4:30 pm Lockett 381

Hui-Hsiung Kuo, Mathematics Department, LSU
Interacting Fock spaces associated with probability measures

Wednesday, September 21, 2005

Posted September 17, 2005

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

Monday, September 26, 2005

Posted September 19, 2005

4:00 pm - 5:00 pm 1030 Magnolia Wood Avenue

Si Si, Aichi Prefectural University, Japan
Some aspects of Poisson noise

Monday, October 3, 2005

Posted September 20, 2005

3:40 pm - 4:30 pm Lockett 381

Jeremy Becnel, Stephen F. Austin State University
Delta Function for an Affine Subspace

Monday, October 10, 2005

Posted October 5, 2005

3:40 pm - 4:30 pm Lockett 381

Jeremy Becnel, Stephen F. Austin State University
The Delta Function for an Affine Subspace II

Wednesday, November 30, 2005

Posted November 9, 2005

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

Monday, March 27, 2006

Posted March 8, 2006

4:40 pm - 5:30 pm Lockett 381

K Saito, Meijo University
Constructions of stochastic processes

Friday, September 29, 2006

Posted September 26, 2006

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

Friday, October 27, 2006

Posted October 12, 2006

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

Habib Ouerdiane, University of Tunis
Infinite Dimensional Complex Analysis, Holomorphy and Application to Gaussian and non Gaussian Analysis

Friday, November 3, 2006

Posted October 31, 2006

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

Friday, November 10, 2006

Posted November 6, 2006

3:40 pm 282, Lockett

Suat Namli, Louisiana State University Graduate Student
A White Noise Analysis Approach to Orthogonal Polynomials

Friday, December 1, 2006

Posted November 28, 2006

3:40 pm Lockett 282

Suat Namli, Louisiana State University Graduate Student
Orthogonal Polynomials of Exponential and Fractional Types and Beyond

Friday, December 8, 2006

Posted December 4, 2006

3:40 pm Lockett 282

Hong Yin, Department of Mathematics, LSU Graduate Student
Backward Stochastic Differential Equations

Tuesday, March 6, 2007

Posted March 2, 2007

4:00 pm Lockett 240

Hong Yin, Department of Mathematics, LSU Graduate Student
Backward Stochastic Differential Equations

Tuesday, March 27, 2007

Posted March 26, 2007

4:00 pm 240 Lockett

Suat Namli, Louisiana State University Graduate Student
Orthogonal polynomials of the exponential and fractional type

Tuesday, April 17, 2007

Posted March 30, 2007

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.

Thursday, April 26, 2007

Posted April 19, 2007

4:00 pm Lockett 240

Walfredo Javier, Department of Mathematics, Southern University
Mutual information of certain multivariate distributions

Thursday, October 4, 2007

Posted October 1, 2007

3:40 pm Lockett 381

Ambar Sengupta, Mathematics Department, LSU
Gaussian Matrix Integrals

Thursday, November 15, 2007

Posted November 12, 2007

3:30 pm Lockett 381

P. Sundar, Department of Mathematics, LSU
Fractional Gaussian integrals

Monday, April 7, 2008

Posted April 7, 2008

3:40 pm Lockett 381

P. Sundar, Department of Mathematics, LSU
On the Martingale Problem

Monday, April 28, 2008

Posted April 25, 2008

3:40 pm Lockett 381

Julius Esunge, Department of Mathematics, LSU Graduate Student
Anticipating Linear SDEs

Monday, September 29, 2008

Posted September 18, 2008

3:40 pm - 4:30 pm Lockett 381

Hui-Hsiung Kuo, Mathematics Department, LSU
The MRM for Orthogonal Polynomials

Monday, October 6, 2008

Posted September 18, 2008

3:40 pm - 4:30 pm Lockett 381

Rahul Roy, Indian Statistical Institute, Delhi
Coverage of space by random sets

Monday, November 17, 2008

Posted October 1, 2008

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

Monday, April 13, 2009

Posted March 30, 2009

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

Friday, September 11, 2009

Posted September 14, 2009

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

Wednesday, September 23, 2009

Posted September 14, 2009

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.

Monday, October 5, 2009

Posted October 4, 2009

3:40 pm - 4:30 pm Lockett 285

On a class of stochastic partial differential equations

Friday, March 26, 2010

Posted February 8, 2010

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).

Monday, May 3, 2010

Posted April 27, 2010

3:40 pm - 4:30 pm Lockett 285

Eric Hillebrand, Economics Department, LSU
Temporal Correlation of Defaults in Subprime Securitization

Monday, September 27, 2010

Posted September 22, 2010

3:40 pm - 4:30 pm 241 Lockett

Benedykt Szozda, Department of Mathematics, LSU
New approach to stochastic integration of anticipating stochastic processes

Friday, December 3, 2010

Posted November 19, 2010

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.

Monday, September 12, 2011

Posted September 9, 2011

3:40 pm - 4:30 pm 240 Lockett

Joonhee Rhee, Soongsil University, South Korea
A Defaultable Bond Pricing under the Change of Filtration

Monday, September 19, 2011

Posted September 16, 2011

3:40 pm - 4:30 pm 240 Lockett

Joonhee Rhee, Soongsil University, South Korea
Defaultable Bond Pricing under a Change of Filtration: Part II

Monday, September 26, 2011

Posted September 24, 2011

3:40 pm - 4:30 pm 240 Lockett

Ambar Sengupta, Mathematics Department, LSU
Model-free Pricing Formulas

Monday, November 7, 2011

Posted November 7, 2011

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.

Monday, November 21, 2011

Posted November 21, 2011

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.

Tuesday, August 21, 2012

Posted August 5, 2012

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

Wednesday, September 12, 2012

Posted September 7, 2012

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.

Monday, October 8, 2012

Posted October 1, 2012

3:30 pm - 4:20 pm Lockett 240

Irina Craciun, Department of Mathematics, LSU Graduate Student
Gaussian Measure for Subspaces of a Banach Space

Tuesday, October 8, 2013

Posted September 11, 2013

3:30 pm - 5:00 pm Lockett 285

Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore
Stopping CCR-flows

Tuesday, November 12, 2013

Posted October 15, 2013

3:30 pm - 4:30 pm Lockett 381

Jimmie Lawson, Mathematics Department, LSU
Random Variables with Values In Nonpositively Curved Metric Spaces

Abstract

Tuesday, November 19, 2013

Posted November 13, 2013

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.

Monday, March 31, 2014

Posted March 31, 2014

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.

Friday, August 21, 2015

Posted March 25, 2015

2:30 pm - 3:20 pm Lockett 284

Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore
Brownian Bridge in Quantum Probability

Monday, September 14, 2015

Posted September 11, 2015

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.

Monday, September 21, 2015

Posted September 20, 2015

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.

Monday, September 28, 2015

Posted September 24, 2015

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.

Monday, October 5, 2015

Posted October 2, 2015

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.

Monday, October 12, 2015

Posted October 9, 2015

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.

Monday, November 16, 2015

Posted November 13, 2015

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)

Monday, November 23, 2015

Posted November 20, 2015

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.

Monday, November 30, 2015

Posted November 28, 2015

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.

Tuesday, March 15, 2016

Posted March 14, 2016

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.

Tuesday, March 29, 2016

Posted March 28, 2016

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.

Tuesday, April 12, 2016

Posted April 11, 2016

3:30 pm - 4:30 pm 244 Lockett

Hui-Hsiung Kuo, Mathematics Department, LSU
Some ideas on extending the Ito theory of stochastic integration

Wednesday, March 15, 2017

Posted March 8, 2017

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.

Wednesday, March 29, 2017

Posted March 9, 2017

3:30 pm - 4:30 pm Lockett 237

Hui-Hsiung Kuo, Mathematics Department, LSU
Ito's formula for adapted and instantly independent stochastic processes

Monday, February 5, 2018

Posted February 4, 2018

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.

Monday, February 19, 2018

Posted February 17, 2018

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.

Monday, February 26, 2018

Posted February 24, 2018

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.

Monday, March 5, 2018

Posted March 3, 2018

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.

Monday, March 12, 2018

Posted March 11, 2018

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".

Monday, April 9, 2018

Posted April 6, 2018

11:00 am - 12:00 pm Lockett 239

Exponential 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.

Monday, April 23, 2018

Posted April 21, 2018

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.

Monday, February 21, 2022

Posted February 14, 2022

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).

Monday, March 21, 2022

Posted March 2, 2022

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.]

Monday, April 4, 2022

Posted February 14, 2022

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.

Monday, April 11, 2022

Posted February 14, 2022

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.

Monday, April 18, 2022

Posted February 14, 2022

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)

Monday, April 25, 2022

Posted March 2, 2022

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.

Monday, February 13, 2023

Posted February 11, 2023

12:45 pm - 2:00 pm Keisler Lounge

Informal discussion on probability research topics

Monday, February 27, 2023

Posted February 11, 2023

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.

Monday, March 6, 2023

Posted March 2, 2023

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.

Monday, March 20, 2023

Posted February 11, 2023

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.

Today, Monday, March 27, 2023

Posted March 2, 2023

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.

Monday, April 3, 2023

Posted February 11, 2023

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.

Monday, April 10, 2023

Posted March 26, 2023

Samy Tindel, Purdue University
TBA

Monday, April 17, 2023

Posted February 11, 2023

1:00 pm - 2:00 pm Zoom

Adina Oprisan, New Mexico State University
TBA