Weak Bernoullicity of random walk in random scenery

Abstract

In this saner, we consider an arbitrary irreducible random walk and an arbitrary stationary and ergodic random scenery on _??_d. We find conditions on their distributions such that the associated random walk in random scenery is or is not weak Bernoulli. Our results extend an earlier classification for the special case in which the individual scenery values are assumed to be independent and identically distributed random variables.