15 July 2024

Department of Mathematics, King’s College London, UK

Organiser: Markus Riedle (KCL)

Large Deviations and Stochastic Control

Amarjit Budhiraja (North Carolina at Chapel Hill, USA)

Heilbronn Distinguished Visiting Fellow, Isaac Newton Institute for Mathematical Sciences, UK

The theory of large deviations has a long history with deep connections to statistical mechanics, information theory, partial differential equations, optimization theory, and mathematical statistics. In recent years an approach for analyzing large deviation asymptotics for stochastic dynamical systems has emerged, that transforms the study of large deviation probabilities to that of the asymptotic behavior of certain stochastic control problems. One of the key advantages of this approach is that, instead of needing to establish exponential probability estimates and comparison principles for Hamilton-Jacobi equations, the main ingredient is proving suitable tightness and weak convergence properties. In this expository talk I will give a high-level overview of this approach and provide a survey of some of the large deviation problems that have been studied using this method.

About the Speaker: Amarjit Budhiraja is a Professor in the Department of Statistics and Operations Research at the University of North Carolina at Chapel Hill. He graduated in 1994 from UNC under the direction of Professor Gopinath Kallianpur. After graduation he did a one year postdoc at Iowa State University, Math Department under Professor Wolfgang Kliemann and then a two year postdoc at Brown University, Division of Applied Mathematics under Professor Harold Kushner. He was a tenure track Assistant Professor at the University of Notre Dame, Department of Mathematics from 1998-2000 and in 2000 he returned to UNC. Amarjit Budhiraja works in probability and stochastic analysis and some of the topics he is interested in are Large Deviations, Stochastic Control, Stochastic Differential Games, Stochastic Networks, Stochastic Partial Differential Equations, Random Graphs, Stochastic Numerics, Nonlinear Filtering. Together with Paul Dupuis he has authored a book on theory and applications of Large Deviations, Analysis and Approximation of Rare Events.

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