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.
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}
}
Comments
33 pages