Further topics on discrete-time Markov control processes:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London
Springer
1999
|
| Series: | Applications of mathematics
42 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 251 - 261 |
| Physical Description: | XII, 276 S. |
| ISBN: | 0387986944 |
Staff View
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| 100 | 1 | |a Hernández-Lerma, Onésimo |d 1946- |e Verfasser |0 (DE-588)111571081 |4 aut | |
| 245 | 1 | 0 | |a Further topics on discrete-time Markov control processes |c Onésimo Hernández-Lerma ; Jean Bernard Lasserre |
| 264 | 1 | |a New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London |b Springer |c 1999 | |
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| 490 | 1 | |a Applications of mathematics |v 42 | |
| 500 | |a Literaturverz. S. 251 - 261 | ||
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| 650 | 7 | |a Controlesystemen |2 gtt | |
| 650 | 7 | |a Markov, Processus de |2 ram | |
| 650 | 7 | |a Markov-processen |2 gtt | |
| 650 | 7 | |a Numerieke wiskunde |2 gtt | |
| 650 | 7 | |a Processos de markov |2 larpcal | |
| 650 | 7 | |a Processos estocásticos |2 larpcal | |
| 650 | 7 | |a Systèmes échantillonnés |2 ram | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Discrete-time systems | |
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Record in the Search Index
| _version_ | 1804127454157078528 |
|---|---|
| adam_text | Contents
Preface vii
7 Ergodicity and Poisson s Equation 1
7.1 Introduction 1
7.2 Weighted norms and signed kernels 2
A. Weighted norm spaces 2
B. Signed kernels 3
C. Contraction maps 5
7.3 Recurrence concepts 7
A. Irreducibility and recurrence 7
B. Invariant measures 8
C. Conditions for irreducibility and recurrence 9
D. w Geometric ergodicity 11
7.4 Examples on w geometric ergodicity 17
7.5 Poisson s equation 24
A. The multichain case 26
B. The unichain P.E 31
C. Examples 34
8 Discounted Dynamic Programming with Weighted Norms 39
8.1 Introduction 39
8.2 The control model and control policies 40
8.3 The optimality equation 43
A. Assumptions 44
B. The discounted cost optimality equation 47
x Contents
C. The dynamic programming operator 48
D. Proof of Theorem 8.3.6 51
8.4 Further analysis of value iteration 55
A. Asymptotic discount optimality 56
B. Estimates of VI convergence 57
C. Rolling horizon procedures 58
D. Forecast horizons and elimination
of non optimal actions 59
8.5 The weakly continuous case 65
8.6 Examples 68
8.7 Further remarks 73
9 The Expected Total Cost Criterion 75
9.1 Introduction 75
9.2 Preliminaries 76
A. Extended real numbers 76
B. Integrability 78
9.3 The expected total cost 79
9.4 Occupation measures 84
A. Expected occupation measures 85
B. The sufficiency problem 88
9.5 The optimality equation 93
A. The optimality equation 93
B. Optimality criteria 95
C. Deterministic stationary policies 100
9.6 The transient case 103
A. Transient models 103
B. Optimality conditions 109
C. Reduction to deterministic policies 110
D. The policy iteration algorithm 113
10 Undiscounted Cost Criteria 117
10.1 Introduction 117
A. Undiscounted criteria 117
B. AC criteria 119
C. Outline of the chapter 120
10.2 Preliminaries 120
A. Assumptions 121
B. Corollaries 123
C. Discussion 124
10.3 From AC optimality to undiscounted criteria 126
A. The AC optimality inequality 128
B. The AC optimality equation 129
C. Uniqueness of the ACOE 131
D. Bias optimal policies 132
Contents xi
E. Undiscounted criteria 135
10.4 Proof of Theorem 10.3.1 137
A. Preliminary lemmas 137
B. Completion of the proof 141
10.5 Proof of Theorem 10.3.6 143
A. Proof of part (a) 143
B. Proof of part (b) 146
C. Policy iteration 146
10.6 Proof of Theorem 10.3.7 149
10.7 Proof of Theorem 10.3.10 150
10.8 Proof of Theorem 10.3.11 154
10.9 Examples 156
11 Sample Path Average Cost 163
11.1 Introduction 163
A. Definitions 163
B. Outline of the chapter 166
11.2 Preliminaries 167
A. Positive Harris recurrence 167
B. Limiting average variance 168
11.3 The w geometrically ergodic case 175
A. Optimality in UDS 177
B. Optimality in II 178
C. Variance minimization 180
D. Proof of Theorem 11.3.5 181
E. Proof of Theorem 11.3.8 185
11.4 Strictly unbounded costs 188
11.5 Examples 196
12 The Linear Programming Approach 203
12.1 Introduction 203
A. Outline of the chapter 204
12.2 Preliminaries 205
A. Dual pairs of vector spaces 205
B. Infinite linear programming 212
C. Approximation of linear programs 214
D. Tightness and invariant measures 215
12.3 Linear programs for the AC problem 218
A. The linear programs 219
B. Solvability of (P) 222
C. Absence of duality gap 224
D. The Farkas alternative 226
12.4 Approximating sequences and strong duality 233
A. Minimizing sequences for (P) 233
B. Maximizing sequences for (P*) 234
xii Contents
12.5 Finite LP approximations 238
A. Aggregation 238
B. Aggregation relaxation 239
C. Aggregation relaxion inner approximations 240
12.6 Proof of Theorems 12.5.3, 12.5.5, 12.5.7 242
References 251
Abbreviations 263
Glossary of notation 265
Index 271
|
| any_adam_object | 1 |
| author | Hernández-Lerma, Onésimo 1946- Lasserre, Jean-Bernard 1953- |
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| author_role | aut aut |
| author_sort | Hernández-Lerma, Onésimo 1946- |
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| building | Verbundindex |
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| ctrlnum | (OCoLC)40654817 (DE-599)BVBBV012782993 |
| dewey-full | 519.2/33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/33 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T18:33:36Z |
| institution | BVB |
| isbn | 0387986944 |
| language | English |
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| physical | XII, 276 S. |
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| series | Applications of mathematics |
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| spelling | Hernández-Lerma, Onésimo 1946- Verfasser (DE-588)111571081 aut Further topics on discrete-time Markov control processes Onésimo Hernández-Lerma ; Jean Bernard Lasserre New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London Springer 1999 XII, 276 S. txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 42 Literaturverz. S. 251 - 261 Commande, Théorie de la ram Controlesystemen gtt Markov, Processus de ram Markov-processen gtt Numerieke wiskunde gtt Processos de markov larpcal Processos estocásticos larpcal Systèmes échantillonnés ram Control theory Discrete-time systems Markov processes Markov-Entscheidungsprozess (DE-588)4168927-6 gnd rswk-swf Diskreter Markov-Prozess (DE-588)4150185-8 gnd rswk-swf Markov-Entscheidungsprozess (DE-588)4168927-6 s Diskreter Markov-Prozess (DE-588)4150185-8 s DE-604 Lasserre, Jean-Bernard 1953- Verfasser (DE-588)121290255 aut Applications of mathematics 42 (DE-604)BV000895226 42 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008694032&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hernández-Lerma, Onésimo 1946- Lasserre, Jean-Bernard 1953- Further topics on discrete-time Markov control processes Applications of mathematics Commande, Théorie de la ram Controlesystemen gtt Markov, Processus de ram Markov-processen gtt Numerieke wiskunde gtt Processos de markov larpcal Processos estocásticos larpcal Systèmes échantillonnés ram Control theory Discrete-time systems Markov processes Markov-Entscheidungsprozess (DE-588)4168927-6 gnd Diskreter Markov-Prozess (DE-588)4150185-8 gnd |
| subject_GND | (DE-588)4168927-6 (DE-588)4150185-8 |
| title | Further topics on discrete-time Markov control processes |
| title_auth | Further topics on discrete-time Markov control processes |
| title_exact_search | Further topics on discrete-time Markov control processes |
| title_full | Further topics on discrete-time Markov control processes Onésimo Hernández-Lerma ; Jean Bernard Lasserre |
| title_fullStr | Further topics on discrete-time Markov control processes Onésimo Hernández-Lerma ; Jean Bernard Lasserre |
| title_full_unstemmed | Further topics on discrete-time Markov control processes Onésimo Hernández-Lerma ; Jean Bernard Lasserre |
| title_short | Further topics on discrete-time Markov control processes |
| title_sort | further topics on discrete time markov control processes |
| topic | Commande, Théorie de la ram Controlesystemen gtt Markov, Processus de ram Markov-processen gtt Numerieke wiskunde gtt Processos de markov larpcal Processos estocásticos larpcal Systèmes échantillonnés ram Control theory Discrete-time systems Markov processes Markov-Entscheidungsprozess (DE-588)4168927-6 gnd Diskreter Markov-Prozess (DE-588)4150185-8 gnd |
| topic_facet | Commande, Théorie de la Controlesystemen Markov, Processus de Markov-processen Numerieke wiskunde Processos de markov Processos estocásticos Systèmes échantillonnés Control theory Discrete-time systems Markov processes Markov-Entscheidungsprozess Diskreter Markov-Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008694032&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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