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

Chen，Anyue1,2

2019

10.1007/s10959-019-00941-w

JOURNAL OF THEORETICAL PROBABILITY   影响因子和分区

0894-9840

1572-9230

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.

Denumerable Markov processes Existence Resolvents Taboo probabilities Transition functions Uniqueness

SCI

英语

第一 ; 通讯

Mathematics

Statistics & Probability

WOS:000581126700010

SPRINGER/PLENUM PUBLISHERS

MATHEMATICS

2-s2.0-85073974107

Scopus

1.Department of MathematicsSouthern University of Science and Technology,Shenzhen,Xueyuan Boulevard 1088,518055,China
2.Department of Mathematical SciencesUniversity of Liverpool,Liverpool,Peach Street,L69 7ZL,United Kingdom

Chen，Anyue. Resolvent Decomposition Theorems and Their Application in Denumerable Markov Processes with Instantaneous States[J]. JOURNAL OF THEORETICAL PROBABILITY,2019,33(4):2089-2118.

Chen，Anyue.(2019).Resolvent Decomposition Theorems and Their Application in Denumerable Markov Processes with Instantaneous States.JOURNAL OF THEORETICAL PROBABILITY,33(4),2089-2118.

Chen，Anyue."Resolvent Decomposition Theorems and Their Application in Denumerable Markov Processes with Instantaneous States".JOURNAL OF THEORETICAL PROBABILITY 33.4(2019):2089-2118.