English

Explosion, implosion, and moments of passage times for continuous-time Markov chains: a semimartingale approach

Probability 2014-07-15 v3 Mathematical Physics math.MP

Abstract

We establish general theorems quantifying the notion of recurrence --- through an estimation of the moments of passage times --- for irreducible continuous-time Markov chains on countably infinite state spaces. Sharp conditions of occurrence of the phenomenon of explosion are also obtained. A new phenomenon of implosion is introduced and sharp conditions for its occurrence are proven. The general results are illustrated by treating models having a difficult behaviour even in discrete time.

Keywords

Cite

@article{arxiv.1202.0952,
  title  = {Explosion, implosion, and moments of passage times for continuous-time Markov chains: a semimartingale approach},
  author = {Mikhail Menshikov and Dimitri Petritis},
  journal= {arXiv preprint arXiv:1202.0952},
  year   = {2014}
}

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33 pages