Grad Student Seminar: Adam Waterbury

Stochastic Approximation of Quasi-Stationary Distributions

We propose two numerical schemes for approximating quasi-stationary distributions (QSD) of finite state Markov chains with absorbing states. Both schemes are described in terms of certain interacting chains in which the interaction is given in terms of the total time occupation measure of all particles in the system. The schemes can be viewed as combining the key features of the two basic simulation-based methods for approximating QSD originating from the works of Fleming and Viot (1979) and Aldous, Flannery, and Palacios (1998), respectively. In this talk I will describe the two schemes, discuss their convergence properties as both time and the number of particles in the system simultaneously become large, and present some exploratory numerical results comparing them to other QSD approximation methods.