Stephen Connor (University of York)

State-dependent Foster-Lyapunov criteria

Foster-Lyapunov drift criteria are a useful way of proving results about the speed of convergence of Markov chains. Most of these criteria involve examining the change in expected value of some function of the chain over one time step. However, in some situations it is more convenient to look at the change in expectation over a longer time period, which perhaps varies with the current state of the chain.

This talk will review some joint work with Gersende Fort (CNRS-TELECOM ParisTech), looking at when such state-dependent drift conditions hold and (perhaps more interestingly) what can be inferred from them. (Sadly I can't promise many pictures on this occasion, but I do promise not to show any proofs!)