Abstract
A random timeT is a future independent μ time for a Markov chain (X n ) 0 ∞ ifT is independent of (X T+n ) /∞ =0 and if (X T+n ) /∞ =0 is a Markov chain with initial distribution μ and the same transition probabilities as (X n ) 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.
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