Bounding Stationary Expectations of Markov Processes

Abstract

This paper develops a simple and systematic approach for obtaining bounds on stationary expectations of Markov processes. Given a function f which one is interested in evaluating, the main idea is to find a function g that satisfies a certain “mean drift” inequality with respect to f, which in turn leads to bounds on the stationary expectation of the latter. The approach developed in the paper is broadly applicable and can be used to bound steady-state expectations in general state space Markov chains, continuous time chains, and diffusion processes (with, or without, reflecting boundaries).