A splitting technique for Harris recurrent Markov chains

Abstract

A technique is presented, which enables the state space of a Harris recurrent Markov chain to be “split” in a way, which introduces into the split state space an “atom”. Hence the full force of renewal theory can be used in the analysis of Markov chains on a general state space. As a first illustration of the method we show how Derman's construction for the invariant measure works in the general state space. The Splitting Technique is also applied to the study of sums of transition probabilities.