DMS Stochastic Analysis Seminar

Speaker: Prof. Andrey Sarantsev, Assistant Professor, University of Nevada, Reno

Title: Markov processes on the half-line with slow convergence

Abstract: Consider a stochastic differential equation with reflection on the half-line. We are interested whether it converges in the long run to its equilibrium (stationary, invariant) distribution, and how fast. Lyapunov functions are a well-developed method to prove such convergence and to establish exponential rate. In this talk, we will discuss a modification of this method which proves long-term convergence but at a rate slower than exponential, for example polynomial. This method can be potentially useful for other state spaces.