On the Nonexplosion and Explosion for Nonhomogeneous Markov Pure Jump Processes
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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.
KeywordsDynkin’s formula Nonhomogeneous Markov pure jump process Nonexplosion
Mathematics Subject Classification (2010)60J75 90C40
I would like to thank Professor Mufa Chen (Beijing Normal University) for providing the scan copy of the relevant pages in  and the paper . I also thank the referees for their helpful comments and remarks. This work was carried out with a financial grant from the Research Fund for Coal and Steel of the European Commission, within the INDUSE-2-SAFETY project (Grant No. RFSR-CT-2014-00025).
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