Markov chains and invariant probabilities:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2003
|
| Series: | Progress in mathematics
211 |
| Subjects: | |
| Online Access: | Table of contents Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 193 - 201 |
| Physical Description: | XVI, 205 S. 24 cm |
| ISBN: | 3764370009 |
Staff View
MARC
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| 245 | 1 | 0 | |a Markov chains and invariant probabilities |c Onésimo Hérnandez-Lerma ; Jean Bernard Lasserre |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2003 | |
| 300 | |a XVI, 205 S. |b 24 cm | ||
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| 490 | 1 | |a Progress in mathematics |v 211 | |
| 500 | |a Literaturverz. S. 193 - 201 | ||
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| 650 | 4 | |a Mesures invariantes | |
| 650 | 7 | |a Processos de markov |2 larpcal | |
| 650 | 7 | |a Processos estocasticos |2 larpcal | |
| 650 | 4 | |a Markov processes | |
| 650 | 4 | |a Invariant measures | |
| 650 | 4 | |a Set functions | |
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Record in the Search Index
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| adam_text | Contents
Acknowledgements ix
Preface xi
Abbreviations and List of Symbols xv
1 Preliminaries 1
1.1 Introduction 1
1.2 Measures and Functions 1
1.3 Weak Topologies 4
1.4 Convergence of Measures 6
1.5 Complements 13
1.6 Notes 17
1 Markov Chains and Ergodicity 19
2 Markov Chains and Ergodic Theorems 21
2.1 Introduction 21
2.2 Basic Notation and Definitions 22
2.3 Ergodic Theorems 28
2.4 The Ergodicity Property 33
2.5 Pathwise Results 36
2.6 Notes 39
3 Countable Markov Chains 41
3.1 Introduction 41
3.2 Classification of States and Class Properties 41
3.3 Limit Theorems 44
3.4 Notes 46
vi Contents
4 Harris Markov Chains 47
4.1 Introduction 47
4.2 Basic Definitions and Properties 47
4.3 Characterization of Harris recurrence 51
4.4 Sufficient Conditions for P.H.R 56
4.5 Harris and Doeblin Decompositions 60
4.6 Notes 61
5 Markov Chains in Metric Spaces 63
5.1 Introduction 63
5.2 The Limit in Ergodic Theorems 64
5.3 Yosida s Ergodic Decomposition 68
5.4 Pathwise Results 73
5.5 Proofs 74
5.6 Notes 82
6 Classification of Markov Chains via Occupation Measures 83
6.1 Introduction 83
6.2 A Classification 84
6.3 On the Birkhoff Individual Ergodic Theorem 88
6.4 Notes 92
II Further Ergodicity Properties 93
7 Feller Markov Chains 95
7.1 Introduction 95
7.2 Weak and Strong Feller Markov Chains 96
7.3 Quasi Feller Chains 99
7.4 Notes 102
8 The Poisson Equation 103
8.1 Introduction 103
8.2 The Poisson Equation 103
8.3 Canonical Pairs 105
8.4 The Cesaro Averages Approach 110
8.5 The Abelian Approach 114
8.6 Notes 119
9 Strong and Uniform Ergodicity 121
9.1 Introduction 121
9.2 Strong and Uniform Ergodicity 122
9.3 Weak and Weak Uniform Ergodicity 127
9.4 Notes 131
Contents vii
III Existence and Approximation of Invariant
Probability Measures 133
10 Existence of Invariant Probability Measures 135
10.1 Introduction and Statement of the Problems 135
10.2 Notation and Definitions 136
10.3 Existence Results 138
10.4 Markov Chains in Locally Compact Separable Metric Spaces . . . 143
10.5 Other Existence Results in Locally Compact
Separable Metric Spaces 145
10.6 Technical Preliminaries 147
10.7 Proofs 149
10.8 Notes 155
11 Existence and Uniqueness of Fixed Points for Markov Operators 157
11.1 Introduction and Statement of the Problems 157
11.2 Notation and Definitions 158
11.3 Existence Results 160
11.4 Proofs 167
11.5 Notes 174
12 Approximation Procedures for Invariant Probability Measures 175
12.1 Introduction 175
12.2 Statement of the Problem and Preliminaries 176
12.3 An Approximation Scheme 178
12.4 A Moment Approach for a Special Class of Markov Chains .... 183
12.5 Notes 190
Bibliography 193
Index 203
|
| any_adam_object | 1 |
| author | Hernández-Lerma, Onésimo 1946- Lasserre, Jean-Bernard 1953- |
| author_GND | (DE-588)111571081 (DE-588)121290255 |
| author_facet | Hernández-Lerma, Onésimo 1946- Lasserre, Jean-Bernard 1953- |
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| author_sort | Hernández-Lerma, Onésimo 1946- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T19:11:31Z |
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| isbn | 3764370009 |
| language | English |
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| physical | XVI, 205 S. 24 cm |
| publishDate | 2003 |
| publishDateSearch | 2003 |
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| spelling | Hernández-Lerma, Onésimo 1946- Verfasser (DE-588)111571081 aut Markov chains and invariant probabilities Onésimo Hérnandez-Lerma ; Jean Bernard Lasserre Basel [u.a.] Birkhäuser 2003 XVI, 205 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 211 Literaturverz. S. 193 - 201 Fonctions d'ensemble Markov, Processus de Markov-processen gtt Mesures invariantes Processos de markov larpcal Processos estocasticos larpcal Markov processes Invariant measures Set functions Markov-Kette (DE-588)4037612-6 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd rswk-swf Markov-Kette (DE-588)4037612-6 s Ergodentheorie (DE-588)4015246-7 s Wahrscheinlichkeitsmaß (DE-588)4137556-7 s DE-604 Lasserre, Jean-Bernard 1953- Verfasser (DE-588)121290255 aut Progress in mathematics 211 (DE-604)BV000004120 211 http://www.loc.gov/catdir/toc/fy038/2003041471.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010211576&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hernández-Lerma, Onésimo 1946- Lasserre, Jean-Bernard 1953- Markov chains and invariant probabilities Progress in mathematics Fonctions d'ensemble Markov, Processus de Markov-processen gtt Mesures invariantes Processos de markov larpcal Processos estocasticos larpcal Markov processes Invariant measures Set functions Markov-Kette (DE-588)4037612-6 gnd Ergodentheorie (DE-588)4015246-7 gnd Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd |
| subject_GND | (DE-588)4037612-6 (DE-588)4015246-7 (DE-588)4137556-7 |
| title | Markov chains and invariant probabilities |
| title_auth | Markov chains and invariant probabilities |
| title_exact_search | Markov chains and invariant probabilities |
| title_full | Markov chains and invariant probabilities Onésimo Hérnandez-Lerma ; Jean Bernard Lasserre |
| title_fullStr | Markov chains and invariant probabilities Onésimo Hérnandez-Lerma ; Jean Bernard Lasserre |
| title_full_unstemmed | Markov chains and invariant probabilities Onésimo Hérnandez-Lerma ; Jean Bernard Lasserre |
| title_short | Markov chains and invariant probabilities |
| title_sort | markov chains and invariant probabilities |
| topic | Fonctions d'ensemble Markov, Processus de Markov-processen gtt Mesures invariantes Processos de markov larpcal Processos estocasticos larpcal Markov processes Invariant measures Set functions Markov-Kette (DE-588)4037612-6 gnd Ergodentheorie (DE-588)4015246-7 gnd Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd |
| topic_facet | Fonctions d'ensemble Markov, Processus de Markov-processen Mesures invariantes Processos de markov Processos estocasticos Markov processes Invariant measures Set functions Markov-Kette Ergodentheorie Wahrscheinlichkeitsmaß |
| url | http://www.loc.gov/catdir/toc/fy038/2003041471.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010211576&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT hernandezlermaonesimo markovchainsandinvariantprobabilities AT lasserrejeanbernard markovchainsandinvariantprobabilities |