Finiteness of hitting times under taboo
Probability
2013-11-25 v1
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. Keywords and phrases: Markov chain, hitting time, taboo probabilities, catalytic branching process.
Keywords
Cite
@article{arxiv.1310.7108,
title = {Finiteness of hitting times under taboo},
author = {Ekaterina Vl. Bulinskaya},
journal= {arXiv preprint arXiv:1310.7108},
year = {2013}
}