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Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Mikhail Menshikov

Menshikov, M.V. & Petritis, D. (2014). Explosion, implosion, and moments of passage times for continuous-time Markov chains: A semimartingale approach. Stochastic Processes and their Applications 124(7): 2388-2414.

Author(s) from Durham

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.