A LIAPOUNOV BOUND FOR SOLUTIONS OF THE POISSON EQUATION

In this paper we consider psi-irreducible Markov processes evolving in discrete or continuous time on a general state space. We develop a Li apounov function criterion that permits one to obtain explicit bounds on the solution to the Poisson equation and, in particular, obtain con ditions under which the solution is square integrable. These results a re applied to obtain sufficient conditions that guarantee the validity of a functional central limit theorem for the Markov process. As a se cond consequence of the bounds obtained, a perturbation theory for Mar kov processes is developed which gives conditions under which both the solution to the Poisson equation and the invariant probability for th e process are continuous functions of its transition kernel. The techn iques are illustrated with applications to queueing theory and autoreg ressive processes.