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Finiteness of hitting times under taboo

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  • Bulinskaya, Ekaterina Vladimirovna

Abstract

We consider a continuous-time Markov chain with a finite or countable state space. For a site y and subset H of the state space, the hitting time of y under taboo H is defined to be infinite if the process trajectory hits H before y, and the first hitting time of y otherwise. We investigate the probability that such times are finite. In particular, if the taboo set is finite, an efficient iterative scheme reduces the study to the known case of a singleton taboo. A similar procedure applies in the case of finite complement of the taboo set. The study is motivated by classification of branching processes with finitely many catalysts.

Suggested Citation

  • Bulinskaya, Ekaterina Vladimirovna, 2014. "Finiteness of hitting times under taboo," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 15-19.
    • Handle: RePEc:eee:stapro:v:85:y:2014:i:c:p:15-19
    DOI: 10.1016/j.spl.2013.10.016
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    Cited by:

    1. Xiang, Xuyan & Fu, Haiqin & Zhou, Jieming & Deng, Yingchun & Yang, Xiangqun, 2021. "Taboo rate and hitting time distribution of continuous-time reversible Markov chains," Statistics & Probability Letters, Elsevier, vol. 169(C).
    2. Bulinskaya, Ekaterina Vl., 2018. "Spread of a catalytic branching random walk on a multidimensional lattice," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2325-2340.

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