Future independent times and Markov chains

Abstract

A random time T is a future independent μ time for a Markov chain (Xn)0∞ if T is independent of (XT+n)n/∞=0 and if (XT+n)n/∞=0 is a Markov chain with initial distribution μ and the same transition probabilities as (Xn)0∞. This concept is used (with μ the "conditional stationary measure") to give a new and short proof of the basic limit theorem of Markov chains, improving somewhat the result in the null-recurrent case. © 1988 Springer-Verlag.