Existence and Uniqueness of Denumerable Markov Processes with Instantaneous States

被引：0

作者：

Wu, Xiaohan ^{[1
,2
,3
]}

Chen, Anyue ^{[4
,5
]}

Li, Junping ^{[6
]}

机构：

[1] Liaocheng Univ, Sch Math Sci, Liaocheng 252059, Peoples R China

[2] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

[3] Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China

[4] Southern Univ Sci & Technol, Dept Math, Xue Yuan Blvd 1088, Shenzhen 518055, Peoples R China

[5] Univ Liverpool, Dept Math Sci, Peach St, Liverpool L69 7ZL, England

[6] Cent South Univ, Sch Math & Stat, Changsha 410083, Peoples R China

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2024年 / 37卷 / 01期

关键词：

Denumerable Markov processes; Transition functions; Resolvent; Taboo probabilities; Existence; Uniqueness; BRANCHING-PROCESSES; RECURRENCE;

D O I：

10.1007/s10959-023-01299-w

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：511 / 532

页数：22

共 50 条

[31] OPTIMIZATION OF DENUMERABLE SEMI-MARKOV DECISION PROCESSES.
Staniewski, Piotr
Weinfeld, Roman
Systems Science, 1980, 6 (02): : 129 - 141
[32] Existence and Uniqueness of Quasi-stationary Distributions for Symmetric Markov Processes with Tightness Property
Masayoshi Takeda
Journal of Theoretical Probability, 2019, 32 : 2006 - 2019
[33] Existence and Uniqueness of Quasi-stationary Distributions for Symmetric Markov Processes with Tightness Property
Takeda, Masayoshi
JOURNAL OF THEORETICAL PROBABILITY, 2019, 32 (04) : 2006 - 2019
[34] TRANSIENT ATOMIC MARKOV-CHAINS WITH A DENUMERABLE NUMBER OF STATES
BREIMAN, L
ANNALS OF MATHEMATICAL STATISTICS, 1958, 29 (01): : 212 - 218
[35] Nonstationary denumerable state Markov decision processes - with average variance criterion
Guo, XP
MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 1999, 49 (01) : 87 - 96
[36] CONTINUITY OF MEAN RECURRENCE TIMES IN DENUMERABLE SEMI-MARKOV PROCESSES
DEPPE, H
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1985, 69 (04): : 581 - 592
[37] THE UNIQUENESS OF SYMMETRIZING MEASURE OF MARKOV PROCESSES
Ying, Jiangang
Zhao, Minzhi
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 138 (06) : 2181 - 2185
[38] DENUMERABLE MARKOV PROCESSES WITH BOUNDED GENERATORS - ROUTINE FOR CALCULATING PIJ INFINITY
JENSEN, A
KENDALL, D
JOURNAL OF APPLIED PROBABILITY, 1971, 8 (02) : 423 - &
[39] Non-ergodicity criteria for denumerable continuous time Markov processes
Choi, BD
Kim, B
OPERATIONS RESEARCH LETTERS, 2004, 32 (06) : 574 - 580
[40] TRUNCATION APPROXIMATION OF LIMIT PROBABILITIES FOR DENUMERABLE SEMI-MARKOV PROCESSES
TWEEDIE, RL
JOURNAL OF APPLIED PROBABILITY, 1975, 12 (01) : 161 - 163

← 1 2 3 4 5 →