Model of Markov chains in space-time random environments

Abstract

A general framework of stochastic model for a Markov chain in a space-time random environment is introduced, here the environment: ξ(superscript *):={ξ(subscript t,x,) t∈N, x∈χ} is a random field. We study the dependence relations between the environment and the original chain, especially the ”feedback”. Some equivalence theorems and law of large numbers are obtained.