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

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 too...

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Bibliographic Details
Published inJournal of theoretical probability Vol. 33; no. 4; pp. 2089 - 2118
Main Author Chen, Anyue
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2020
Springer Nature B.V
Subjects
Decomposition
Markov analysis
Markov processes
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
Theorems
Uniqueness
Primary 60J27
Taboo probabilities
Uniqueness
Transition functions
Denumerable Markov processes
Secondary 60J35
Resolvents
Existence
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Summary: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.
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-019-00941-w