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Existence Condition of Strong Stationary Times for Continuous Time Markov Chains on Discrete Graphs

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  • Guillaume Copros

    (Institut de Mathématiques de Toulouse)

Abstract

We consider a random walk on a discrete connected graph having some infinite branches plus finitely many vertices with finite degrees. We find the generator of a strong stationary dual in the sense of Fill, and use it to find some equivalent condition to the existence of a strong stationary time. This strong stationary dual process lies in the set of connected compact sets of the compactification of the graph. When the graph is $$\mathbb Z$$ Z , the set here is simply the set of (possibly infinite) segments of $$\mathbb Z$$ Z .

Suggested Citation

  • Guillaume Copros, 2018. "Existence Condition of Strong Stationary Times for Continuous Time Markov Chains on Discrete Graphs," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1679-1728, September.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:3:d:10.1007_s10959-017-0746-4
    DOI: 10.1007/s10959-017-0746-4
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    References listed on IDEAS

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    1. Yu Gong & Yong-Hua Mao & Chi Zhang, 2012. "Hitting Time Distributions for Denumerable Birth and Death Processes," Journal of Theoretical Probability, Springer, vol. 25(4), pages 950-980, December.
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