The existence of moments for stationary Markov chains

Abstract

We give conditions under which the stationary distributionπof a Markov chain admits moments of the general form ∫f(x)π(dx), wherefis a general function; specific examples includef(x) =xrandf(x) =esx. In general the time-dependent moments of the chain then converge to the stationary moments. We show that in special cases this convergence of moments occurs at a geometric rate. The results are applied to random walk on [0, ∞).