Quasi-Stationary Distributions: Markov Chains, Diffusions and Dynamical Systems
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
|
| Schriftenreihe: | Probability and its Applications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XV, 280 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 3642331300 9783642331305 |
Internformat
MARC
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| 245 | 1 | 0 | |a Quasi-Stationary Distributions |b Markov Chains, Diffusions and Dynamical Systems |c Pierre Collet ; Servet Martínez ; Jaime San Martín |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2013 | |
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| 689 | 0 | 0 | |a Markov-Kette |0 (DE-588)4037612-6 |D s |
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| 700 | 1 | |a Martínez, Servet |e Verfasser |4 aut | |
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Datensatz im Suchindex
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IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 QUASI-STATIONARY DISTRIBUTIONS 1
1.2 MARKOV CHAINS 2
1.3 DIFFUSIONS 7
1.4 DYNAMICAL SYSTEMS 9
2 QUASI-STATIONARY DISTRIBUTIONS: GENERAL RESULTS 17
2.1 NOTATION 17
2.2 KILLED PROCESS AND QSD 18
2.3 EXPONENTIAL KILLING 19
2.4 INDEPENDENCE BETWEEN THE EXIT TIME AND THE EXIT STATE 21
2.5 RESTRICTING THE EXIT STATE 22
2.6 CHARACTERIZATION O F QSD BY THE SEMIGROUP 24
2.7 CONTINUITY ASSUMPTIONS 26
3 MARKOV CHAINS ON FINITE SPACES 31
3.1 EXISTENCE OF A QSD 31
3.2 THE CHAIN O F TRAJECTORIES THAT SURVIVE FOREVER 34
3.3 SYMMETRIC CASE 36
3.4 CONDITIONS FOR LUMPING 38
3.5 EXAMPLE: FINITE KILLED RANDOM WALK 4 0
3.6 THE CENTRAL LIMIT THEOREM FOR A QSD 4 2
4 MARKOV CHAINS ON COUNTABLE SPACES 45
4.1 THE MINIMAL PROCESS 45
4.2 THE EXPONENTIAL KILLING CONDITION 47
4.3 THE INFINITESIMAL CHARACTERIZATION OF A QSD 48
4.4 CONDITIONS FOR EXISTENCE OF A QSD 52
4.4.1 THE RESURRECTED PROCESS 53
4.4.2 THE PROOF 54
4.5 KINGMAN'S PARAMETER AND EXPONENTIAL RATE OF SURVIVAL 57
4.6 SYMMETRIC CASE 62
X I I I
HTTP://D-NB.INFO/1024863832
IMAGE 2
XIV CONTENTS
4.7 COMPARISON OF EXPONENTIAL RATES FOR A MONOTONE PROCESS 66
5 BIRTH-AND-DEATH CHAINS 69
5.1 PARAMETERS FOR THE DESCRIPTION O F THE CHAIN 69
5.2 POLYNOMIALS, REPRESENTATION AND DUALITY 72
5.3 STRUCTURE OF THE SET O F QSDS 79
5.4 THE QUASI-LIMITING DISTRIBUTION 83
5.5 THE SURVIVAL PROCESS AND ITS CLASSIFICATION 85
5.6 COMPARISON O F QSDS 93
5.7 ACTION ON AND DISCRETE SPECTRUM 95
5.8 THE PROCESS CONDITIONED TO HITTING BARRIERS 104
5.9 EXAMPLES 105
5.9.1 THE RANDOM WALK 105
5.9.2 THE LINEAR BIRTH-AND-DEATH CHAIN 106
5.9.3 THE M / M / O O QUEUE 106
5.10 STRUCTURED BIRTH-AND-DEATH PROCESSES WITH MUTATIONS 107
6 REGULAR DIFFUSIONS ON [0, OO) 113
6.1 HYPOTHESES AND NOTATIONS 113
6.1.1 QSDS ON A BOUNDED INTERVAL 117
6.2 QSDS ON [0, OO) 126
6.2.1 EXISTENCE AND REGULARITY O F A KERNEL WITH RESPECT TO /N . . 130
6.2.2 A RATIO LIMIT FOR THE DIFFUSION ON (0, OO) 139
6.2.3 THE CASE A (OO) OO 140
6.2.4 THE CASE Y\(OO) = OO 142
6.3 CHARACTERIZATION OF THE QSD FAMILY 157
6.4 FT-PROCESSES ASSOCIATED TO X 159
6.5 /?-POSITIVITY FOR X 162
6.5.1 ^-CLASSIFICATION 167
6.6 DOMAIN O F ATTRACTION FOR A QSD 179
6.7 EXAMPLES 191
6.7.1 DRIFT EVENTUALLY CONSTANT 191
6.7.2 X CAN BE /^-POSITIVE 195
6.7.3 X = OO FOR SOME BOUNDED DRIFTS 195
7 INFINITY AS ENTRANCE BOUNDARY 197
7.1 INTRODUCTION 197
7.2 BASIC PROPERTIES OF X 198
7.3 SPECTRAL THEORY 200
7.4 SUFFICIENT CONDITIONS FOR INTEGRABILITY OF 204
7.5 QSD AND YAGLOM LIMIT 208
7.5.1 SPEED OF CONVERGENCE TO THE YAGLOM LIMIT 211
7.6 THE Q-PROCESS 213
7.7 UNIQUENESS O F QSD 214
7.8 EXAMPLES 221
7.8.1 A BIOLOGICAL MODEL 221
7.8.2 SHIRYAEV MARTINGALE 222
IMAGE 3
CONTENTS XV
8 DYNAMICAL SYSTEMS 227
8.1 SOME GENERAL RESULTS 227
8.1.1 COUNTEREXAMPLES 231
8.2 GIBBS MEASURES AND QSDS 231
8.2.1 NOTATIONS AND GIBBS MEASURES 232
8.2.2 GIBBS QSD 236
8.3 PIANIGIANI-YORKE QSD 249
8.3.1 AN APPLICATION TO THE NEWTON METHOD 262
8.4 OTHER RESULTS 266
8.4.1 OTHER PROOFS 266
8.4.2 ABSOLUTELY CONTINUOUS QSD 267
8.4.3 PROPERTIES OF A QSD 267
8.4.4 DECAY O F PROBABILITIES 267
REFERENCES 269
INDEX 275
TABLE O F NOTATIONS 277
CITATIONS INDEX 279 |
| any_adam_object | 1 |
| author | Collet, Pierre 1948- Martínez, Servet San Martín, Jaime |
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| author_facet | Collet, Pierre 1948- Martínez, Servet San Martín, Jaime |
| author_role | aut aut aut |
| author_sort | Collet, Pierre 1948- |
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| dewey-full | 519.233 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.233 |
| dewey-search | 519.233 |
| dewey-sort | 3519.233 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| isbn | 3642331300 9783642331305 |
| language | English |
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| physical | XV, 280 S. graph. Darst. 235 mm x 155 mm |
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| spelling | Collet, Pierre 1948- Verfasser (DE-588)131528122 aut Quasi-Stationary Distributions Markov Chains, Diffusions and Dynamical Systems Pierre Collet ; Servet Martínez ; Jaime San Martín Berlin [u.a.] Springer 2013 XV, 280 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Probability and its Applications Dynamisches System (DE-588)4013396-5 gnd rswk-swf Diffusionsprozess (DE-588)4274463-5 gnd rswk-swf Markov-Kette (DE-588)4037612-6 gnd rswk-swf Markov-Kette (DE-588)4037612-6 s Diffusionsprozess (DE-588)4274463-5 s Dynamisches System (DE-588)4013396-5 s DE-604 Martínez, Servet Verfasser aut San Martín, Jaime Verfasser aut Erscheint auch als Online-Ausgabe 978-3-642-33131-2 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4096299&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025417781&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Collet, Pierre 1948- Martínez, Servet San Martín, Jaime Quasi-Stationary Distributions Markov Chains, Diffusions and Dynamical Systems Dynamisches System (DE-588)4013396-5 gnd Diffusionsprozess (DE-588)4274463-5 gnd Markov-Kette (DE-588)4037612-6 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4274463-5 (DE-588)4037612-6 |
| title | Quasi-Stationary Distributions Markov Chains, Diffusions and Dynamical Systems |
| title_auth | Quasi-Stationary Distributions Markov Chains, Diffusions and Dynamical Systems |
| title_exact_search | Quasi-Stationary Distributions Markov Chains, Diffusions and Dynamical Systems |
| title_full | Quasi-Stationary Distributions Markov Chains, Diffusions and Dynamical Systems Pierre Collet ; Servet Martínez ; Jaime San Martín |
| title_fullStr | Quasi-Stationary Distributions Markov Chains, Diffusions and Dynamical Systems Pierre Collet ; Servet Martínez ; Jaime San Martín |
| title_full_unstemmed | Quasi-Stationary Distributions Markov Chains, Diffusions and Dynamical Systems Pierre Collet ; Servet Martínez ; Jaime San Martín |
| title_short | Quasi-Stationary Distributions |
| title_sort | quasi stationary distributions markov chains diffusions and dynamical systems |
| title_sub | Markov Chains, Diffusions and Dynamical Systems |
| topic | Dynamisches System (DE-588)4013396-5 gnd Diffusionsprozess (DE-588)4274463-5 gnd Markov-Kette (DE-588)4037612-6 gnd |
| topic_facet | Dynamisches System Diffusionsprozess Markov-Kette |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4096299&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025417781&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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