Existence and Uniqueness of Denumerable Markov Processes with Instantaneous States

Xiaohan Wu (), Anyue Chen () and Junping Li ()
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Xiaohan Wu: Liaocheng University
Anyue Chen: Southern University of Science and Technology
Junping Li: Central South University

Journal of Theoretical Probability, 2024, vol. 37, issue 1, 511-532

Abstract: Abstract Based on the resolvent decomposition theorems presented very recently by Chen (J Theor Probab 33:2089–2118, 2020), in this paper we focus on investigating the fundamental problems of existence and uniqueness criteria for Denumerable Markov Processes with finitely many instantaneous states. Some elegant sufficient and necessary conditions are obtained for this less-investigated topic. A few important examples including the generalized Kolmogorov models are presented to illustrate our general results.

Keywords: Denumerable Markov processes; Transition functions; Resolvent; Taboo probabilities; Existence; Uniqueness; Primary 60J27; Secondary 60J35 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-023-01299-w

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