RANDOM COEFFICIENT AUTOREGRESSIVE PROCESSES:A MARKOV CHAIN ANALYSIS OF STATIONARITY AND FINITENESS OF MOMENTS

We give conditions under which the stationary distribution π of a Markov chain admits moments of the general form ∫ f ( x ) π ( dx ), where f is a general function; specific examples include f ( x ) = x r and f ( x ) = e sx . 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, ∞).