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Future independent times and Markov chains

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A random timeT is a future independent μ time for a Markov chain (X n ) 0 ifT is independent of (X T+n ) n /∞ =0 and if (X T+n ) 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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This work was supported by the Swedish Natural Science Research Council and done while the author was visiting the Department of Statistics, Stanford University

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Thorisson, H. Future independent times and Markov chains. Probab. Th. Rel. Fields 78, 143–148 (1988).

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Key words

  • Markov chain
  • future independent time
  • regeneration
  • stationary measure
  • coupling