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Future independent times and Markov chains
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  • Published: March 1988

Future independent times and Markov chains

  • Hermann Thorisson1 

Probability Theory and Related Fields volume 78, pages 143–148 (1988)Cite this article

Summary

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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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Chalmers University of Technology, S-412 96, Göteborg, Sweden

    Hermann Thorisson

Authors
  1. Hermann Thorisson
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Additional information

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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Cite this article

Thorisson, H. Future independent times and Markov chains. Probab. Th. Rel. Fields 78, 143–148 (1988). https://doi.org/10.1007/BF00718042

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  • Received: 04 March 1986

  • Revised: 12 November 1987

  • Issue Date: March 1988

  • DOI: https://doi.org/10.1007/BF00718042

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Key words

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