On the nonexplosion and explosion for nonhomogeneous Markov pure jump processes

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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Cited by in corpus (1)

• Note on discounted continuous-time Markov decision processes with a lower bounding function