Probability Seminar
Questions or comments?

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

Probability Seminar
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Posted October 15, 2003

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

Stochastic Navier-Stokes

Probability Seminar
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Posted November 11, 2003

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

Probability Seminar
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Posted November 18, 2003

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

The Radon-Gauss Transform

Probability Seminar
Questions or comments?

Posted March 3, 2004

Last modified March 20, 2004

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

Probability Seminar
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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

Probability Seminar
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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

Probability Seminar
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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

Probability Seminar
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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

Probability Seminar
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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

Probability Seminar
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Posted September 19, 2005

Last modified September 26, 2005

Si Si, Aichi Prefectural University, Japan

Some apects of Poisson noise

Probability Seminar
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Posted September 20, 2005

Last modified September 22, 2005

Jeremy Becnel, Stephen F. Austin State University

Delta Function for an Affine Subspace

Probability Seminar
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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

Probability Seminar
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Posted November 9, 2005

Last modified November 22, 2005

Jeremy Becnel, Stephen F. Austin State University

An Infinite Dimensional Integral Identity for the Segal-Bargmann Transform

Probability Seminar
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Posted March 8, 2006

Last modified March 27, 2006

K Saito, Meijo University

Constructions of stochastic processes associated

Probability Seminar
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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

Probability Seminar
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Posted October 12, 2006

Last modified October 20, 2006

Habib Ouerdiane, University of Tunis

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

Probability Seminar
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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

Probability Seminar
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Posted November 6, 2006

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

A White Noise Analysis Approach to Orthogonal Polynomials

Probability Seminar
Questions or comments?

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

Probability Seminar
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Posted December 4, 2006

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

Backward Stochastic Differential Equations

Probability Seminar
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Posted March 2, 2007

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

Backward Stochastic Differential Equations

Probability Seminar
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Posted March 26, 2007

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

Orthogonal polynomials of the exponential and fractional type

Probability Seminar
Questions or comments?

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.

Probability Seminar
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Posted April 19, 2007

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

Mutual information of certain multivariate distributions

Probability Seminar
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Posted October 1, 2007

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

Gaussian Matrix Integrals

Probability Seminar
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Posted November 12, 2007

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

Fractional Gaussian integrals

Probability Seminar
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Posted April 7, 2008

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

On the Martingale Problem

Probability Seminar
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Posted April 25, 2008

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

Anticipating Linear SDEs

Probability Seminar
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Posted September 18, 2008

Last modified September 19, 2008

Hui-Hsiung Kuo, Mathematics Department, LSU

The MRM for Orthogonal Polynomials

Probability Seminar
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Posted September 18, 2008

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

Coverage of space by random sets

Probability Seminar
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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

Probability Seminar
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Posted March 30, 2009

Last modified April 13, 2009

Jeremy Becnel, Stephen F. Austin State University

Forming the Radon Transform and Support Theorem in Infinite Dimensions

Probability Seminar
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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

Probability Seminar
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Posted September 14, 2009

Last modified September 23, 2009

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.

Probability Seminar
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Posted October 4, 2009

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

On a class of stochastic partial differential equations

Probability Seminar
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Posted February 8, 2010

Last modified March 16, 2010

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).

Probability Seminar
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Posted April 27, 2010

Last modified April 29, 2010

Eric Hillebrand, Economics Department, LSU

Temporal Correlation of Defaults in Subprime Securitization

Probability Seminar
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Posted September 22, 2010

Last modified September 24, 2010

Benedykt Szozda, Department of Mathematics, LSU

New approach to stochastic integration of anticipating stochastic processes

Probability Seminar
Questions or comments?

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.

Probability Seminar
Questions or comments?

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

Probability Seminar
Questions or comments?

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

Probability Seminar
Questions or comments?

Posted September 24, 2011

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

Model-free Pricing Formulas

Probability Seminar
Questions or comments?

Posted November 7, 2011

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

Anticipative Stochastic Integral and Near-Martingales

Abstract: 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 It\^o, 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 It\^o 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.

Probability Seminar
Questions or comments?

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.

Probability Seminar
Questions or comments?

Posted August 5, 2012

Last modified August 21, 2012

Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore

Trotter Product Formula for Stochastic Evolutions in Fock space

Probability Seminar
Questions or comments?

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.

Probability Seminar
Questions or comments?

Posted October 1, 2012

Last modified October 8, 2012

Irina Craciun, Department of Mathematics, LSU
Graduate Student

Gaussian Measure for Subspaces of a Banach Space

Probability Seminar
Questions or comments?

Posted September 11, 2013

Last modified September 15, 2013

Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore

Stopping CCR-flows

Probability Seminar
Questions or comments?

Posted October 15, 2013

Last modified November 9, 2013

Jimmie Lawson, Mathematics Department, LSU

Random Variables with Values In Nonpositively Curved Metric Spaces

Probability Seminar
Questions or comments?

Posted November 13, 2013

Last modified July 26, 2015

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.

Probability Seminar
Questions or comments?

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.

Probability Seminar
Questions or comments?

Posted March 25, 2015

Last modified August 19, 2015

Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore

Brownian Bridge in Quantum Probability

Probability Seminar
Questions or comments?

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.

Probability Seminar
Questions or comments?

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.

Probability Seminar
Questions or comments?

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.

Probability Seminar
Questions or comments?

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.

Probability Seminar
Questions or comments?

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.

Probability Seminar
Questions or comments?

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)

Probability Seminar
Questions or comments?

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.

Probability Seminar
Questions or comments?

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.

Probability Seminar
Questions or comments?

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.

Probability Seminar
Questions or comments?

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.

Probability Seminar
Questions or comments?

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

Probability Seminar
Questions or comments?

Posted March 8, 2017

Last modified March 13, 2017

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.

Probability Seminar
Questions or comments?

Posted March 9, 2017

Last modified March 13, 2017

Hui-Hsiung Kuo, Mathematics Department, LSU

Ito's formula for adapted and instantly independent stochastic processes

Probability Seminar
Questions or comments?

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.

Probability Seminar
Questions or comments?

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.

Probability Seminar
Questions or comments?

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.

Probability Seminar
Questions or comments?

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.

Probability Seminar
Questions or comments?

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".

Probability Seminar
Questions or comments?

Posted April 6, 2018

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.

Probability Seminar
Questions or comments?

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.