On the nonexplosion and explosion for nonhomogeneous Markov pure jump processes

2015/11/16 by Yi Zhang, Zhang, Yi · 1 citation
Economics, Econometrics and Finance · Mathematics · #60J75. 90C40 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1511.05011

openalex publication_date 2015/11/16 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain new drift-type conditions for nonexplosion and explosion for nonhomogeneous Markov pure jump processes in Borel state spaces. The conditions are sharp; e.g., the one for nonexplosion is necessary if the state space is in addition locally compact and the Q-function satisfies weak Feller-type and local boundedness conditions. We comment on the relations of our conditions with the existing ones in the literature, and demonstrate some possible applications.

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