RECURRENCE CONDITIONS FOR MARKOV DECISION PROCESSES WITH BOREL STATE SPACE: A SURVEY

被引：41

作者：

Hernandez-Lerma, Onesimo ^{[1
]}

Montes-De-Oca, Raul ^{[2
]}

Cavazos-Cadena, Rolando ^{[3
]}

机构：

[1] CINVESTAV IPN, Dept Matemat, Mexico City 07000, DF, Mexico

[2] Univ Autonoma Metropolitana, Dept Matemat, Unidad Iztapalapa, Mexico City 09340, DF, Mexico

[3] Univ Autonoma Agr Antonio Narro, Dept Estadist & Calculo, Saltillo 25315, Coahuila, Mexico

来源：

ANNALS OF OPERATIONS RESEARCH | 1991年 / 28卷 / 01期

关键词：

D O I：

10.1007/BF02055573

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

This paper describes virtually all the recurrence conditions used heretofore for Markov decision processes with Borel state and action spaces, which include some forms of mixing and contraction properties, Doeblin's condition, Harris recurrence, strong ergodicity, and the existence of bounded solutions to the optimality equation for average reward processes. The aim is to establish (when possible) implications and equivalences between these conditions.

引用

页码：29 / 46

页数：18

共 39 条

[1]

[Anonymous], 1984, GEN IRREDUCIBLE MARK

[2]

Assaf D., 1980, Stochastic Processes & their Applications, V10, P313, DOI 10.1016/0304-4149(80)90014-9

[3] CONTROLLED SEMI-MARKOV MODELS UNDER LONG-RUN AVERAGE REWARDS [J].

BHATTACHARYA, RN ;

MAJUMDAR, M .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1989, 22 (02) :223-242

[4]

Cavazos-Cadena R., APPL MATH O IN PRESS

[5] NECESSARY AND SUFFICIENT CONDITIONS FOR A BOUNDED SOLUTION TO THE OPTIMALITY EQUATION IN AVERAGE REWARD MARKOV DECISION CHAINS [J].

CAVAZOSCADENA, R .

SYSTEMS & CONTROL LETTERS, 1988, 10 (01) :71-78

[6] DENUMERABLE STATE MARKOVIAN DECISION PROCESSES - AVERAGE COST CRITERION [J].

DERMAN, C .

ANNALS OF MATHEMATICAL STATISTICS, 1966, 37 (06) :1545-&

[7]

Doob J. L., 1953, STOCHASTIC PROCESSES

[8]

DOUKHAN P, 1980, CR ACAD SCI A MATH, V290, P921

[9]

Dynkin EB, 1979, CONTROLLED MARKOV PR

[10] NOTE ON SIMULTANEOUS RECURRENCE CONDITIONS ON A SET OF DENUMERABLE STOCHASTIC MATRICES [J].

FEDERGRUEN, A ;

HORDIJK, A ;

TIJMS, HC .

JOURNAL OF APPLIED PROBABILITY, 1978, 15 (04) :842-847

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