Topics in the constructive theory of countable Markov chains:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1995
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | 169 S. graph. Darst. |
| ISBN: | 0521461979 9780521461979 |
Staff View
MARC
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| 245 | 1 | 0 | |a Topics in the constructive theory of countable Markov chains |c G. Fayolle ; V. A. Malyshev ; M. V. Menshikov |
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Record in the Search Index
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| adam_text | Contents
Introduction and history page 1
1 Preliminaries 5
1.1 Irreducibility and aperiodicity 6
1.2 Classification 8
1.3 Continuous time 9
1.4 Classical examples 11
1.4.1 Doeblin s condition 11
1.4.2 Birth and death process 12
1.4.3 The space homogeneous random walk on Zm 13
2 General criteria 16
2.1 Criteria involving semi martingales 16
2.2 Criteria for countable Markov chains 26
3 Explicit construction of Lyapounov functions 33
3.1 Markov chains in a half strip 33
3.1.1 Generalizations and problems 35
3.2 Random walks in Z+: main definitions and interpretation 37
3.3 Classification of random walks in 7?+ 39
3.4 Zero drifts 56
3.5 Jackson networks 62
3.6 Asymptotically small drifts 72
3.7 Stability and invariance principle 76
4 Ideology of induced chains 79
4.1 Second vector field 79
4.2 Classification of paths 82
4.3 Gluing Lyapounov functions together 86
4.4 Classification in Z% 92
Contents
5 Random walks in two dimensional complexes 98
5.1 Introduction and preliminary results 98
5.2 Random walks on hedgehogs 103
5.3 Formulation of the main result 104
5.4 Quasi deterministic process 108
5.5 Proof of the ergodicity in theorem 5.3.4 111
5.6 Proof of the transience 114
5.7 Proof of the recurrence 118
5.8 Proof of the non ergodicity 121
5.9 Queueing applications 123
5.10 Remarks and problems 130
6 Stability 131
6.1 A necessary and sufficient condition for continuity 131
6.2 Continuity of stationary probabilities 137
6.3 Continuity of random walks in Z^ 144
7 Exponential convergence and analyticity 148
7.1 Analytic Lyapounov families 148
7.2 Proof of the exponential convergence 150
7.3 General analyticity theorem 157
7.4 Proof of analyticity completed 161
7.5 Examples of analyticity 163
Bibliography 165
Index 168
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| author | Fayolle, Guy 1943- Malyšev, Vadim Aleksandrovič Menšikov, Michail Vasilʹevič |
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| indexdate | 2024-07-09T17:51:08Z |
| institution | BVB |
| isbn | 0521461979 9780521461979 |
| language | English |
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| spelling | Fayolle, Guy 1943- Verfasser (DE-588)120682036 aut Topics in the constructive theory of countable Markov chains G. Fayolle ; V. A. Malyshev ; M. V. Menshikov 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1995 169 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Markov, processus de ram Markov processes Markov-Kette (DE-588)4037612-6 gnd rswk-swf Endliche Markov-Kette (DE-588)4152154-7 gnd rswk-swf Ljapunov-Funktion (DE-588)4274502-0 gnd rswk-swf Endliche Markov-Kette (DE-588)4152154-7 s DE-604 Markov-Kette (DE-588)4037612-6 s Ljapunov-Funktion (DE-588)4274502-0 s DE-188 Malyšev, Vadim Aleksandrovič Verfasser (DE-588)1104397889 aut Menšikov, Michail Vasilʹevič Verfasser (DE-588)1067821546 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006896171&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fayolle, Guy 1943- Malyšev, Vadim Aleksandrovič Menšikov, Michail Vasilʹevič Topics in the constructive theory of countable Markov chains Markov, processus de ram Markov processes Markov-Kette (DE-588)4037612-6 gnd Endliche Markov-Kette (DE-588)4152154-7 gnd Ljapunov-Funktion (DE-588)4274502-0 gnd |
| subject_GND | (DE-588)4037612-6 (DE-588)4152154-7 (DE-588)4274502-0 |
| title | Topics in the constructive theory of countable Markov chains |
| title_auth | Topics in the constructive theory of countable Markov chains |
| title_exact_search | Topics in the constructive theory of countable Markov chains |
| title_full | Topics in the constructive theory of countable Markov chains G. Fayolle ; V. A. Malyshev ; M. V. Menshikov |
| title_fullStr | Topics in the constructive theory of countable Markov chains G. Fayolle ; V. A. Malyshev ; M. V. Menshikov |
| title_full_unstemmed | Topics in the constructive theory of countable Markov chains G. Fayolle ; V. A. Malyshev ; M. V. Menshikov |
| title_short | Topics in the constructive theory of countable Markov chains |
| title_sort | topics in the constructive theory of countable markov chains |
| topic | Markov, processus de ram Markov processes Markov-Kette (DE-588)4037612-6 gnd Endliche Markov-Kette (DE-588)4152154-7 gnd Ljapunov-Funktion (DE-588)4274502-0 gnd |
| topic_facet | Markov, processus de Markov processes Markov-Kette Endliche Markov-Kette Ljapunov-Funktion |
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