Future independent times and Markov chains (Q1092518)

A random time T is a future independent \(\mu\) time for a Markov chain \((X_ n)_ 0^{\infty}\) if T is independent of \((X_{T+n})^{\infty}_{n=0}\) and if \((X_{T+n})^{\infty}_{n=0}\) is a Markov chain with initial distribution \(\mu\) and the same transition probabilities as \((X_ n)_ 0^{\infty}\). This concept is used (with \(\mu\) 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.