The quasi-stationary distribution (QSD) of a Markov process X(t) with respect to a set D characterizes the distribution of X(T) given that X(t) remains in D for t∈[0,T] and T is large. Although they have a long history in probability, QSDs are not nearly as well understood as their (linear) cousins, stationary distributions. The first half of the talk will review some of the subtleties in characterizing, analyzing and computing QSDs. The second half will present a recently derived mapping between QSDs and ergodic optimal control problems and describe how the control representation can be used to resolve some of these difficulties.
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Professor Paul Dupuis is the IBM Professor of Applied Mathematics in the Division of Applied Mathematics at Brown University. He is a leader in the field of probability theory and its applications. In particular, in the areas of control of deterministic and stochastic processes, in the mathematics of rare events, as well as in numerical methods such as Markov chain approximations and Monte Carlo simulation, and partial differential equations. He is visiting the Department of Mathematics and Statistics at UMass for the Fall of 2022.