Title: Large Deviations for Empirical Measures of Self-Interacting Markov Chains
Speaker: Adam Waterbury (Denison)
Speaker's URL: https://denison.edu/people/adam-waterbury
Abstract: Self-interacting Markov chains arise in a range of models and applications. For example, they can be used to approximate the quasi-stationary distributions of irreducible Markov chains and to model random walks with edge or vertex reinforcement. The term self-interacting Markov chain is something of a misnomer, as such processes interact with their full path history at each time instant, and therefore are non-Markovian. Under conditions on the self-interaction mechanism, we establish a large deviation principle for the empirical measure of self-interacting chains on finite spaces. In this setting, the rate function takes a strikingly different form than the classical Donsker-Varadhan rate function associated with the empirical measure of a Markov chain; the rate function for self-interacting chains is typically non-convex and is given through a dynamical variational formula with an infinite horizon discounted objective function. This is based on joint work with Amarjit Budhiraja and Pavlos Zoubouloglou.
URL associated with Seminar: https://u.osu.edu/probability/autumn-2023/
