Mathematics Colloquium
Amarjit Budhiraja
University of North Carolina at Chapel Hill
Title: Numerical Approaches for Computing Quasi-stationary Distributions
Date: Friday, November 04, 2022
Place and Time: LOV 101, 3:05-3:55 pm
Abstract.
Markov processes with absorbing states occur frequently in epidemiology, statistical physics, population biology, and other areas. Quasi-stationary distributions (QSD) are the basic mathematical object used to describe the long-time behavior of such Markov processes on non-absorption events. Just as stationary distributions of ergodic Markov processes make the law of the Markov process, initialized at that distribution, invariant at all times, quasi-stationary distributions are probability measures that leave the conditional law of the Markov process, on the event of non-absorption, invariant. In this talk I will present a couple of numerical approaches for approximating QSD for Markov processes. These approaches use ideas from reinforced random walks, interacting particle systems, stochastic approximations and stochastic control theory.