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The cover time of a (multiple) Markov chain with rational transition probabilities is rational

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  • Sylvester, John

Abstract

The cover time of a Markov chain on a finite state space is the expected time until all states are visited. We show that if the cover time of a discrete-time Markov chain with rational transitions probabilities is bounded, then it is a rational number. The result is proved by relating the cover time of the original chain to the hitting time of a set in another higher dimensional chain. We prove this result in a more general setting where k≥1 independent copies of a Markov chain are run simultaneously on the same state space.

Suggested Citation

  • Sylvester, John, 2022. "The cover time of a (multiple) Markov chain with rational transition probabilities is rational," Statistics & Probability Letters, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:stapro:v:187:y:2022:i:c:s016771522200102x
    DOI: 10.1016/j.spl.2022.109534
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    Cited by:

    1. Shengwang Bao & Fan Yang, 2022. "Spatio-Temporal Dynamic of the Land Use/Cover Change and Scenario Simulation in the Southeast Coastal Shelterbelt System Construction Project Region of China," Sustainability, MDPI, vol. 14(14), pages 1-19, July.

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