Holdings: Markov decision processes with their applications

Markov decision processes with their applications:

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Bibliographic Details
Main Authors:	Hu, Qiying (Author), Yue, Wuyi (Author)
Format:	Book
Language:	English
Published:	New York, NY Springer 2008
Series:	Advances in Mechanics and Mathematics 14
Subjects:	Markov-processen Prise de décision (Statistique) Processus de Markov Systèmes échantillonnés - Modèles mathématiques Mathematisches Modell Discrete-time systems > Mathematical models Markov processes Statistical decision Markov-Entscheidungsprozess
Online Access:	Inhaltsverzeichnis
Physical Description:	XIV, 297 S. graph. Darst.
ISBN:	9780387369501 9780387369518

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adam_text	MARKOV DECISION PROCESSES WITH THEIR APPLICATIONS BY PROF. PH.D. QIYING HU FUDAN UNIVERSITY, CHINA PROF. PH.D. WUYI YUE KONAN UNIVERSITY, JAPAN SPRINGER CONTENTS LIST OF FIGURES IX LIST OF TABLES XI PREFACE XIII ACKNOWLEDGMENTS XV 1. INTRODUCTION 1 1 A BRIEF DESCRIPTION OF MARKOV DECISION PROCESSES 1 2 OVERVIEW OF THE BOOK 4 3 ORGANIZATION OF THE BOOK 6 2. DISCRETE TIME MARKOV DECISION PROCESSES: TOTAL RE WARD 11 1 MODEL AND PRELIMINARIES 11 1.1 SYSTEM MODEL 11 1.2 SOMECONCEPTS 12 1.3 FINITENESS OF THE REWARD 14 2 OPTIMALITY EQUATION 17 2.1 VALIDITY OF THE OPTIMALITY EQUATION 17 2.2 PROPERTIES OF THE OPTIMALITY EQUATION 21 3 PROPERTIES OF OPTIMAL POLICIES 25 4 SUCCESSIVE APPROXIMATION 30 5 SUFFICIENT CONDITIONS 32 6 NOTES AND REFERENCES 34 3. DISCRETE TIME MARKOV DECISION PROCESSES: AVERAGE CRITERION 39 1 MODEL AND PRELIMINARIES 39 2 OPTIMALITY EQUATION 43 VI MARKOV DECISION PROCESSES WITH THEIR APPLICATIONS 2.1 PROPERTIES OF ACOE AND OPTIMAL POLICIES 44 2.2 SUFFICIENT CONDITIONS 48 2.3 RECURRENT CONDITIONS 50 3 OPTIMALITY INEQUALITIES 53 3.1 CONDITIONS 54 3.2 PROPERTIES OF ACOI AND OPTIMAL POLICIES 57 4 NOTES AND REFERENCES 60 4. CONTINUOUS TIME MARKOV DECISION PROCESSES 63 1 A STATIONARY MODEL: TOTAL REWARD 63 1.1 MODEL AND CONDITIONS 63 1.2 MODEL DECOMPOSITION 67 1.3 SOME PROPERTIES 71 1.4 OPTIMALITY EQUATION AND OPTIMAL POLICIES 77 2 A NONSTATIONARY MODEL: TOTAL REWARD 85 2.1 MODEL AND CONDITIONS 85 2.2 OPTIMALITY EQUATION 87 3 A STATIONARY MODEL: AVERAGE CRITERION 95 4 NOTES AND REFERENCES 101 5. SEMI-MARKOV DECISION PROCESSES 105 1 MODEL AND CONDITIONS 105 1.1 MODEL 105 1.2 REGULAER CONDITIONS 107 1.3 CRITERIA 110 2 TRANSFORMATION 111 2.1 TOTAL REWARD 112 2.2 AVERAGE CRITERION 115 3 NOTES AND REFERENCES 119 6. MARKOV DECISION PROCESSES IN SEMI-MARKOV ENVIRONMENTS 121 1 CONTINUOUS TIME MDP IN SEMI-MARKOV ENVIRONMENTS 121 1.1 MODEL 121 1.2 OPTIMALITY EQUATION 127 1.3 APPROXIMATION BY WEAK CONVERGENCE 137 1.4 MARKOV ENVIRONMENT 140 1.5 PHASE TYPE ENVIRONMENT 143 2 SMDP IN SEMI-MARKOV ENVIRONMENTS 148 CONTENTS VN 2.1 MODEL 148 2.2 OPTIMALITY EQUATION 152 2.3 MARKOV ENVIRONMENT 158 3 MIXED MDP IN SEMI-MARKOV ENVIRONMENTS 160 3.1 MODEL 160 3.2 OPTIMALITY EQUATION 163 3.3 MARKOV ENVIRONMENT 170 4 NOTES AND REFERENCES 174 7. OPTIMAL CONTROL OF DISCRETE EVENT SYSTEMS: I 177 1 SYSTEM MODEL 177 2 OPTIMALITY 180 2.1 MAXIMUM DISCOUNTED TOTAL REWARD 182 2.2 MINIMUM DISCOUNTED TOTAL REWARD 186 3 OPTIMALITY IN EVENT FEEDBACK CONTROL 186 4 LINK TO LOGIC LEVEL 189 5 RESOURCE ALLOCATION SYSTEM 194 6 NOTES AND REFERENCES 201 8. OPTIMAL CONTROL OF DISCRETE EVENT SYSTEMS: II 203 1 SYSTEM MODEL 203 2 OPTIMALITY EQUATION AND OPTIMAL SUPERVISORS 207 3 LANGUAGE PROPERTIES 213 4 SYSTEM BASED ON AUTOMATON 215 5 SUPERVISORY CONTROL PROBLEMS 218 5.1 EVENT FEEDBACK CONTROL 218 5.2 STATE FEEDBACK CONTROL 222 6 JOB-MATCHING PROBLEM 223 7 NOTES AND REFERENCES 230 9. OPTIMAL REPLACEMENTUNDERSTOCHASTIC ENVIRONMENTS 233 1 OPTIMAL REPLACEMENT: DISCRETE TIME 234 1.1 PROBLEM AND MODEL 234 1.2 TOTAL COST CRITERION 238 1.3 AVERAGE CRITERION 241 2 OPTIMAL REPLACEMENT: SEMI-MARKOV PROCESSES 244 VIII MARKOV DECISION PROCESSES WITH THEIR APPLICATIONS 2.1 PROBLEM 244 2.2 OPTIMAL CONTROL LIMIT POLICIES 247 2.3 MARKOV ENVIRONMENT 250 2.4 NUMERICAL EXAMPLE 258 3 NOTES AND REFERENCES 260 10. OPTIMAL ALLOCATION IN SEQUENTIAL ONLINE AUCTIONS 265 1 PROBLEM AND MODEL 265 2 ANALYSIS FOR PRIVATE RESERVE PRICE 267 3 ANALYSIS FOR ANNOUNCED RESERVE PRICE 271 4 MONOTONE PROPERTIES 273 5 NUMERICAL RESULTS 282 6 NOTES AND REFERENCES 284 REFERENCES 287 INDEX 295
adam_txt	MARKOV DECISION PROCESSES WITH THEIR APPLICATIONS BY PROF. PH.D. QIYING HU FUDAN UNIVERSITY, CHINA PROF. PH.D. WUYI YUE KONAN UNIVERSITY, JAPAN SPRINGER CONTENTS LIST OF FIGURES IX LIST OF TABLES XI PREFACE XIII ACKNOWLEDGMENTS XV 1. INTRODUCTION 1 1 A BRIEF DESCRIPTION OF MARKOV DECISION PROCESSES 1 2 OVERVIEW OF THE BOOK 4 3 ORGANIZATION OF THE BOOK 6 2. DISCRETE TIME MARKOV DECISION PROCESSES: TOTAL RE WARD 11 1 MODEL AND PRELIMINARIES 11 1.1 SYSTEM MODEL 11 1.2 SOMECONCEPTS 12 1.3 FINITENESS OF THE REWARD 14 2 OPTIMALITY EQUATION 17 2.1 VALIDITY OF THE OPTIMALITY EQUATION 17 2.2 PROPERTIES OF THE OPTIMALITY EQUATION 21 3 PROPERTIES OF OPTIMAL POLICIES 25 4 SUCCESSIVE APPROXIMATION 30 5 SUFFICIENT CONDITIONS 32 6 NOTES AND REFERENCES 34 3. DISCRETE TIME MARKOV DECISION PROCESSES: AVERAGE CRITERION 39 1 MODEL AND PRELIMINARIES 39 2 OPTIMALITY EQUATION 43 VI MARKOV DECISION PROCESSES WITH THEIR APPLICATIONS 2.1 PROPERTIES OF ACOE AND OPTIMAL POLICIES 44 2.2 SUFFICIENT CONDITIONS 48 2.3 RECURRENT CONDITIONS 50 3 OPTIMALITY INEQUALITIES 53 3.1 CONDITIONS 54 3.2 PROPERTIES OF ACOI AND OPTIMAL POLICIES 57 4 NOTES AND REFERENCES 60 4. CONTINUOUS TIME MARKOV DECISION PROCESSES 63 1 A STATIONARY MODEL: TOTAL REWARD 63 1.1 MODEL AND CONDITIONS 63 1.2 MODEL DECOMPOSITION 67 1.3 SOME PROPERTIES 71 1.4 OPTIMALITY EQUATION AND OPTIMAL POLICIES 77 2 A NONSTATIONARY MODEL: TOTAL REWARD 85 2.1 MODEL AND CONDITIONS 85 2.2 OPTIMALITY EQUATION 87 3 A STATIONARY MODEL: AVERAGE CRITERION 95 4 NOTES AND REFERENCES 101 5. SEMI-MARKOV DECISION PROCESSES 105 1 MODEL AND CONDITIONS 105 1.1 MODEL 105 1.2 REGULAER CONDITIONS 107 1.3 CRITERIA 110 2 TRANSFORMATION 111 2.1 TOTAL REWARD 112 2.2 AVERAGE CRITERION 115 3 NOTES AND REFERENCES 119 6. MARKOV DECISION PROCESSES IN SEMI-MARKOV ENVIRONMENTS 121 1 CONTINUOUS TIME MDP IN SEMI-MARKOV ENVIRONMENTS 121 1.1 MODEL 121 1.2 OPTIMALITY EQUATION 127 1.3 APPROXIMATION BY WEAK CONVERGENCE 137 1.4 MARKOV ENVIRONMENT 140 1.5 PHASE TYPE ENVIRONMENT 143 2 SMDP IN SEMI-MARKOV ENVIRONMENTS 148 CONTENTS VN 2.1 MODEL 148 2.2 OPTIMALITY EQUATION 152 2.3 MARKOV ENVIRONMENT 158 3 MIXED MDP IN SEMI-MARKOV ENVIRONMENTS 160 3.1 MODEL 160 3.2 OPTIMALITY EQUATION 163 3.3 MARKOV ENVIRONMENT 170 4 NOTES AND REFERENCES 174 7. OPTIMAL CONTROL OF DISCRETE EVENT SYSTEMS: I 177 1 SYSTEM MODEL 177 2 OPTIMALITY 180 2.1 MAXIMUM DISCOUNTED TOTAL REWARD 182 2.2 MINIMUM DISCOUNTED TOTAL REWARD 186 3 OPTIMALITY IN EVENT FEEDBACK CONTROL 186 4 LINK TO LOGIC LEVEL 189 5 RESOURCE ALLOCATION SYSTEM 194 6 NOTES AND REFERENCES 201 8. OPTIMAL CONTROL OF DISCRETE EVENT SYSTEMS: II 203 1 SYSTEM MODEL 203 2 OPTIMALITY EQUATION AND OPTIMAL SUPERVISORS 207 3 LANGUAGE PROPERTIES 213 4 SYSTEM BASED ON AUTOMATON 215 5 SUPERVISORY CONTROL PROBLEMS 218 5.1 EVENT FEEDBACK CONTROL 218 5.2 STATE FEEDBACK CONTROL 222 6 JOB-MATCHING PROBLEM 223 7 NOTES AND REFERENCES 230 9. OPTIMAL REPLACEMENTUNDERSTOCHASTIC ENVIRONMENTS 233 1 OPTIMAL REPLACEMENT: DISCRETE TIME 234 1.1 PROBLEM AND MODEL 234 1.2 TOTAL COST CRITERION 238 1.3 AVERAGE CRITERION 241 2 OPTIMAL REPLACEMENT: SEMI-MARKOV PROCESSES 244 VIII MARKOV DECISION PROCESSES WITH THEIR APPLICATIONS 2.1 PROBLEM 244 2.2 OPTIMAL CONTROL LIMIT POLICIES 247 2.3 MARKOV ENVIRONMENT 250 2.4 NUMERICAL EXAMPLE 258 3 NOTES AND REFERENCES 260 10. OPTIMAL ALLOCATION IN SEQUENTIAL ONLINE AUCTIONS 265 1 PROBLEM AND MODEL 265 2 ANALYSIS FOR PRIVATE RESERVE PRICE 267 3 ANALYSIS FOR ANNOUNCED RESERVE PRICE 271 4 MONOTONE PROPERTIES 273 5 NUMERICAL RESULTS 282 6 NOTES AND REFERENCES 284 REFERENCES 287 INDEX 295
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spelling	Hu, Qiying Verfasser aut Markov decision processes with their applications by Qiying Hu ; Wuyi Yue New York, NY Springer 2008 XIV, 297 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advances in Mechanics and Mathematics 14 Markov-processen gtt Prise de décision (Statistique) Processus de Markov Systèmes échantillonnés - Modèles mathématiques Mathematisches Modell Discrete-time systems Mathematical models Markov processes Statistical decision Markov-Entscheidungsprozess (DE-588)4168927-6 gnd rswk-swf Markov-Entscheidungsprozess (DE-588)4168927-6 s DE-604 Yue, Wuyi Verfasser aut Advances in Mechanics and Mathematics 14 (DE-604)BV017903734 14 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016301298&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Hu, Qiying Yue, Wuyi Markov decision processes with their applications Advances in Mechanics and Mathematics Markov-processen gtt Prise de décision (Statistique) Processus de Markov Systèmes échantillonnés - Modèles mathématiques Mathematisches Modell Discrete-time systems Mathematical models Markov processes Statistical decision Markov-Entscheidungsprozess (DE-588)4168927-6 gnd
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title	Markov decision processes with their applications
title_auth	Markov decision processes with their applications
title_exact_search	Markov decision processes with their applications
title_exact_search_txtP	Markov decision processes with their applications
title_full	Markov decision processes with their applications by Qiying Hu ; Wuyi Yue
title_fullStr	Markov decision processes with their applications by Qiying Hu ; Wuyi Yue
title_full_unstemmed	Markov decision processes with their applications by Qiying Hu ; Wuyi Yue
title_short	Markov decision processes with their applications
title_sort	markov decision processes with their applications
topic	Markov-processen gtt Prise de décision (Statistique) Processus de Markov Systèmes échantillonnés - Modèles mathématiques Mathematisches Modell Discrete-time systems Mathematical models Markov processes Statistical decision Markov-Entscheidungsprozess (DE-588)4168927-6 gnd
topic_facet	Markov-processen Prise de décision (Statistique) Processus de Markov Systèmes échantillonnés - Modèles mathématiques Mathematisches Modell Discrete-time systems Mathematical models Markov processes Statistical decision Markov-Entscheidungsprozess
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volume_link	(DE-604)BV017903734
work_keys_str_mv	AT huqiying markovdecisionprocesseswiththeirapplications AT yuewuyi markovdecisionprocesseswiththeirapplications

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