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On a New Characterization of Harris Recurrence for Markov Chains and Processes

Author

Listed:
  • Peter Glynn

    (Department of Management Science and Engineering, Stanford University, Stanford, CA 94305, USA)

  • Yanlin Qu

    (Department of Management Science and Engineering, Stanford University, Stanford, CA 94305, USA)

Abstract

This paper shows that Harris recurrent Markov chains and processes can be characterized as the class of Markov chains and processes for which there exists a random time T at which the distribution of the chain or process does not depend on its initial condition. In particular, no independence assumptions concerning the post- T process or T play a role in the characterization. Since Harris chains and processes are known to contain infinite sequences of regeneration times exhibiting various independence properties, it follows that the existence of this single T implies the existence of infinitely many times at which regeneration occurs.

Suggested Citation

  • Peter Glynn & Yanlin Qu, 2023. "On a New Characterization of Harris Recurrence for Markov Chains and Processes," Mathematics, MDPI, vol. 11(9), pages 1-7, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2165-:d:1139609
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    References listed on IDEAS

    as
    1. Vladimir V. Kalashnikov, 1994. "Topics on regenerative processes," International Journal of Stochastic Analysis, Hindawi, vol. 7, pages 1-1, January.
    2. Karl Sigman, 1990. "One-Dependent Regenerative Processes and Queues in Continuous Time," Mathematics of Operations Research, INFORMS, vol. 15(1), pages 175-189, February.
    3. Haya Kaspi & Avi Mandelbaum, 1994. "On Harris Recurrence in Continuous Time," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 211-222, February.
    4. Vladimir V. Kalashnikov, 1994. "Regeneration and general Markov chains," International Journal of Stochastic Analysis, Hindawi, vol. 7, pages 1-15, January.
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