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Journal of Theoretical Probability

, Volume 31, Issue 3, pp 1322–1355 | Cite as

On the Nonexplosion and Explosion for Nonhomogeneous Markov Pure Jump Processes

  • Yi Zhang
Article
  • 92 Downloads

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.

Keywords

Dynkin’s formula Nonhomogeneous Markov pure jump process Nonexplosion 

Mathematics Subject Classification (2010)

60J75 90C40 

Notes

Acknowledgements

I would like to thank Professor Mufa Chen (Beijing Normal University) for providing the scan copy of the relevant pages in [30] and the paper [29]. 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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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of LiverpoolLiverpoolUK

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