Growth rates of sample covariances of stationary symmetric α-stable processes associated with null recurrent Markov chains

Abstract

A null recurrent Markov chain is associated with a stationary mixing S αS process. The resulting process exhibits such strong dependence that its sample covariance grows at a surprising rate which is slower than one would expect based on the fatness of the marginal distribution tails. An additional feature of the process is that the sample autocorrelations converge to non-random limits.