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On the Nonexplosion and Explosion for Nonhomogeneous Markov Pure Jump Processes

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  • Yi Zhang

    (University of Liverpool)

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.

Suggested Citation

  • Yi Zhang, 2018. "On the Nonexplosion and Explosion for Nonhomogeneous Markov Pure Jump Processes," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1322-1355, September.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:3:d:10.1007_s10959-017-0763-3
    DOI: 10.1007/s10959-017-0763-3
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    References listed on IDEAS

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    1. F. M. Spieksma, 2016. "Kolmogorov forward equation and explosiveness in countable state Markov processes," Annals of Operations Research, Springer, vol. 241(1), pages 3-22, June.
    2. Xianping Guo, 2007. "Continuous-Time Markov Decision Processes with Discounted Rewards: The Case of Polish Spaces," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 73-87, February.
    3. V. Rykov & M. Yu. Kitaev, 1995. "Controlled queueing systems," International Journal of Stochastic Analysis, Hindawi, vol. 8, pages 1-3, January.
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