Resolvent Decomposition Theorems and Their Application in Denumerable Markov Processes with Instantaneous States

Anyue Chen ()
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Anyue Chen: Southern University of Science and Technology

Journal of Theoretical Probability, 2020, vol. 33, issue 4, 2089-2118

Abstract: Abstract The basic aim of this paper is to provide a fundamental tool, the resolvent decomposition theorem, in the construction theory of denumerable Markov processes. We present a detailed analytic proof of this extremely useful tool and explain its clear probabilistic interpretation. We then apply this tool to investigate the basic problems of existence and uniqueness criteria for denumerable Markov processes with instantaneous states to which few results have been obtained even until now. Although the complete answers regarding these existence and uniqueness criteria will be given in a subsequent paper, we shall, in this paper, present part solutions of these very important problems that are closely linked with the subtle Williams S and N conditions.

Keywords: Denumerable Markov processes; Transition functions; Resolvents; Taboo probabilities; Existence; Uniqueness; Primary 60J27; Secondary 60J35 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00941-w

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