Markov chains and stochastic stability:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London u.a.
Springer
1996
|
| Ausgabe: | 3. printing |
| Schriftenreihe: | Communications and control engineering series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 550 S. graph. Darst. |
| ISBN: | 3540198326 0387198326 |
Internformat
MARC
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| 245 | 1 | 0 | |a Markov chains and stochastic stability |c S. P. Meyn and R. L. Tweedie |
| 250 | |a 3. printing | ||
| 264 | 1 | |a London u.a. |b Springer |c 1996 | |
| 300 | |a XVI, 550 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1823026257105780736 |
|---|---|
| adam_text |
S.P. MEYN AND R.L. TWEEDIE
MARKOV CHAINS AND
STOCHASTIC
STABILITY
WITH 24 FIGURES
SPRINGER-VERLAG
LONDON
BERLIN HEIDELBERG NEW YORK
PARIS
TOKYO HONG KONG
BARCELONA
BUDAPEST
TABLE
OF CONTENTS
I COMMUNICATION AND REGENERATION 1
1 HEURISTICS 3
1.1 A RANGE OF MARKOVIAN ENVIRONMENTS 3
1.2 BASIC MODELS IN PRACTICE 6
1.3 STOCHASTIC STABILITY FOR MARKOV MODELS 15
1.4 COMMENTARY 21
2 MARKOV MODELS 23
2.1 MARKOV MODELS IN TIME SERIES 24
2.2 NONLINEAR STATE SPACE MODELS 28
2.3 MODELS IN CONTROL AND SYSTEMS THEORY 36
2.4 MARKOV MODELS WITH REGENERATION TIMES 43
2.5 COMMENTARY 52
3 TRANSITION PROBABILITIES 54
3.1 DEFINING A MARKOVIAN PROCESS 55
3.2 FOUNDATIONS ON A COUNTABLE SPACE 57
3.3 SPECIFIC TRANSITION MATRICES 60
3.4 FOUNDATIONS FOR GENERAL STATE SPACE CHAMS 65
3.5 BUILDING TRANSITION KERNELS FOR SPECIFIC MODELS 73
3.6 COMMENTARY 78
4 IRREDUCIBILITY 80
4.1 COMMUNICATION AND IRREDUCIBILITY: COUNTABLE SPACES 81
4.2 V-IRREDUCIBILITY 86
4.3 ^-IRREDUCIBILITY FOR RANDOM WALK MODELS 92
4.4 V'-IRREDUCIBLE LINEAR MODELS 94
4.5 COMMENTARY 98
5 PSEUDO-ATOMS 100
5.1 SPLITTING ^-IRREDUCIBLE CHAINS 101
5.2 SMALL SETS 106
5.3 SMALL SETS FOR SPECIFIC MODELS 110
5.4 CYCLIC BEHAVIOR 114
XIV
TABLE
OP CONTENTS
5.5 PETITE SETS AND SAMPLED CHAMS 119
5.6 COMMENTARY 125
6 TOPOLOGY AND CONTINUITY 126
6.1 FELLER PROPERTIES AND FORMS OF STABILITY 128
6.2 T-CHAINS 133
6.3 CONTINUOUS COMPONENTS FOR SPECIFIC MODELS 137
6.4 E-CHAINS 143
6.5 COMMENTARY 147
7 THE NONLINEAR STATE SPACE MODEL 149
7.1 FORWARD ACCESSIBILITY AND CONTINUOUS COMPONENTS 150
7.2 MINIMAL SETS AND IRREDUCIBILITY 157
7.3 PERIODICITY FOR NONLINEAR STATE SPACE MODEIS 160
7.4 FORWARD ACCESSIBLE EXAMPLES 164
7.5 EQUICONTINUITY AND THE NONLINEAR STATE SPACE MODEL 166
7.6 COMMENTARY 168
II STABILITY STRUCTURES 171
8 TRANSIENCE AND RECURRENCE 173
8.1 CLASSIFYING CHAINS ON COUNTABLE SPACES 175
8.2 CLASSIFYING Y-IRREDUCIBLE CHAINS 179
8.3 RECURRENCE AND TRANSIENCE RELATIONSHIPS 184
8.4 CLASSIFICATION USING DRIFT CRITERIA 189
8.5 CLASSIFYING RANDOM WALK ON 1R+ 194
8.6 COMMENTARY 199
9 HARRIS AND TOPOLOGICAL RECURRENCE 200
9.1 HARRIS RECURRENCE 201
9.2 NON-EVANESCENT AND RECURRENT CHAINS 206
9.3 TOPOLOGICALLY RECURRENT AND TRANSIENT STATES 209
9.4 CRITERIA FOR STABILITY ON A TOPOLOGICAL SPACE 214
9.5 STOCHASTIC COMPAXISON AND INCREMENT ANALYSIS 219
9.6 COMMENTARY 228
10 THE EXISTENCE OF
W
229
10.1 STATIONARITY AND INVARIANCE 230
10.2 THE EXISTENCE OF JR: CHAINS WITH ATOMS 234
10.3 INVARIANT MEASURES: COUNTABLE SPACE MODEIS 236
10.4 THE EXISTENCE OF
T:
V"-IRREDUCIBLE CHAINS 240
10.5 INVARIANT MEASURES: GENERAL MODELS 246
10.6 COMMENTARY 252
11 DRIFT AND REGULARITY 255
11.1 REGULAER CHAINS 257
11.2 DRIFT, HITTING TIMES AND DETERMINISTIC MODEIS 259
11.3 DRIFT CRITERIA FOR REGULARITY 262
11.4 USING THE REGULARITY CRITERIA 270
TABLE OF CONTENTS XV
11.5 EVALUATING NON-POSITIVITY 276
11.6 COMMENTARY 282
12 INVARIANCE AND TIGHTNESS 285
12.1 CHAINS BOUNDED IN PROBABILITY 286
12.2 GENERAIIZED SAMPLING AND INVARIANT MEASURES 289
12.3 THE EXISTENCE OF A A-UENITE INVARIANT MEASURE 294
12.4 INVARIANT MEASURES FOR E-CHAINS 297
12.5 ESTABLISHING BOUNDEDNESS IN PROBABILITY 301
12.6 COMMENTARY 305
FFL
CONVERGENCE
307
13 ERGODICITY 309
13.1 ERGODIC CHAINS ON COUNTABLE SPACES 312
13.2 RENEWAL AND REGENERATION 316
13.3 ERGODICITY OF POSITIVE HARRIS CHAINS 322
13.4 SUMS OF TRANSITION PROBABILITIES 325
13.5 COMMENTARY 328
14 /-ERGODICITY AND /-REGULARITY 330
14.1 /-PROPERTIES: CHAINS WITH ATOMS 332
14.2 /-REGULARITY AND DRIFT 336
14.3 /-ERGODICITY FOR GENERAL CHAINS 342
14.4 /-ERGODICITY OF SPECIFIC MODEIS 346
14.5 A KEY RENEWAL THEOREM 347
14.6 COMMENTARY 352
15 GEOMETRIE ERGODICITY 354
15.1 GEOMETRIE PROPERTIES: CHAINS WITH ATOMS 356
15.2 KENDALI SETS AND DRIFT CRITERIA 363
15.3 /-GEOMETRIE REGULARITY OF
P
AND #
N
371
15.4 /-GEOMETRIE ERGODICITY FOR GENERAL CHAINS 374
15.5 SIMPLE RANDOM WALK AND LINEAR MODEIS 378
15.6 COMMENTARY 381
16 F-UNIFORM ERGODICITY 382
16.1 OPERATOR NORM CONVERGENCE 385
16.2 UNIFORM ERGODICITY 390
16.3 GEOMETRIE ERGODICITY AND INCREMENT ANALYSIS 396
16.4 MODELS FROM QUEUING THEORY 400
16.5 AUTOREGRESSIVE AND STATE SPACE MODEIS 403
16.6 COMMENTARY 407
17 SAMPLE PATHS AND LIMIT THEOREMS 410
17.1 INVARIANT R-FIELDS AND THE LLN 412
17.2 ERGODIC THEOREMS FOR CHAINS POSSESSING AN ATOM 417
17.3 GENERAL HARRIS CHAINS 421
17.4 THE FUNCTIONAL CLT 431
XVI
TABLE
OF CONTENTS
17.5 CRITERIA FOR THE CLT AND THE LIL 438
17.6 APPLICATIONS 441
17.7 COMMENTARY 444
18 POSITIVITY 446
18.1 NULL RECURRENT CHAINS 448
18.2 CHARACTERIZING POSITIVITY USING
P
N
452
18.3 POSITIVITY AND T-CHAINS 455
18.4 POSITIVITY AND E-CHAINS 457
18.5 THE LLN FOR E-CHAINS 461
18.6 COMMENTARY 463
19 GENERALIZED CLASSIFICATION CRITERIA 465
19.1 STATE-DEPENDENT DRIFTS 466
19.2 HISTORY-DEPENDENT DRIFT CRITERIA 474
19.3 MIXED DRIFT CONDITIONS 481
19.4 COMMENTARY 490
IV APPENDICES 493
A MUD MAPS 496
A.L RECURRENCE VERSUS TRANSIENCE 496
A.2 POSITIVITY VERSUS NULLITY 498
A.3 CONVERGENCE PROPERTIES 500
B TESTING FOR STABILITY 501
B.L A GLOSSARY OF DRIFT CONDITIONS 501
B.2 THE SCALAX SETAR MODEL: A COMPLETE CLASSIFICATION 503
C A GLOSSARY OF MODEL ASSUMPTIONS 506
C.L REGENERATIVE MODELS 506
C.2 STATE SPACE MODELS 509
D SOME MATHEMATICAL BACKGROUND . 515
D.L SOME MEASURE THEORY 515
D.2 SOME PROBABILITY THEORY 518
D.3 SOME TOPOLOGY 519
D.4 SOME REAL ANALYSIS 520
D.5 SOME CONVERGENCE CONCEPTS FOR MEASURES 521
D.6 SOME MARTINGALE THEORY 524
D.7 SOME RESULTS ON SEQUENCES AND NUMBERS 526
REFERENCES 528
INDEX 541
SYMBOL INDEX 547 |
| any_adam_object | 1 |
| author | Meyn, Sean P. 1958- Tweedie, Richard L. |
| author_GND | (DE-588)113538537 (DE-588)113538545 |
| author_facet | Meyn, Sean P. 1958- Tweedie, Richard L. |
| author_role | aut aut |
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| building | Verbundindex |
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| callnumber-sort | QA 3274.7 M49 41993 |
| callnumber-subject | QA - Mathematics |
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| dewey-full | 519.233 519.2/3320 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-sort | 3519.233 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. printing |
| format | Book |
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| id | DE-604.BV010762281 |
| illustrated | Illustrated |
| indexdate | 2025-02-03T09:01:59Z |
| institution | BVB |
| isbn | 3540198326 0387198326 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007186502 |
| oclc_num | 243830422 |
| open_access_boolean | |
| owner | DE-12 DE-703 DE-91G DE-BY-TUM DE-384 DE-521 DE-11 |
| owner_facet | DE-12 DE-703 DE-91G DE-BY-TUM DE-384 DE-521 DE-11 |
| physical | XVI, 550 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series2 | Communications and control engineering series |
| spelling | Meyn, Sean P. 1958- Verfasser (DE-588)113538537 aut Markov chains and stochastic stability S. P. Meyn and R. L. Tweedie 3. printing London u.a. Springer 1996 XVI, 550 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Communications and control engineering series Markov processes Zustandsraum (DE-588)4132647-7 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Markov-Kette (DE-588)4037612-6 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Markov-Kette (DE-588)4037612-6 s DE-604 Zeitreihenanalyse (DE-588)4067486-1 s 1\p DE-604 Markov-Prozess (DE-588)4134948-9 s 2\p DE-604 Zustandsraum (DE-588)4132647-7 s 3\p DE-604 Tweedie, Richard L. Verfasser (DE-588)113538545 aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007186502&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Meyn, Sean P. 1958- Tweedie, Richard L. Markov chains and stochastic stability Markov processes Zustandsraum (DE-588)4132647-7 gnd Markov-Prozess (DE-588)4134948-9 gnd Markov-Kette (DE-588)4037612-6 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4132647-7 (DE-588)4134948-9 (DE-588)4037612-6 (DE-588)4067486-1 |
| title | Markov chains and stochastic stability |
| title_auth | Markov chains and stochastic stability |
| title_exact_search | Markov chains and stochastic stability |
| title_full | Markov chains and stochastic stability S. P. Meyn and R. L. Tweedie |
| title_fullStr | Markov chains and stochastic stability S. P. Meyn and R. L. Tweedie |
| title_full_unstemmed | Markov chains and stochastic stability S. P. Meyn and R. L. Tweedie |
| title_short | Markov chains and stochastic stability |
| title_sort | markov chains and stochastic stability |
| topic | Markov processes Zustandsraum (DE-588)4132647-7 gnd Markov-Prozess (DE-588)4134948-9 gnd Markov-Kette (DE-588)4037612-6 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Markov processes Zustandsraum Markov-Prozess Markov-Kette Zeitreihenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007186502&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT meynseanp markovchainsandstochasticstability AT tweedierichardl markovchainsandstochasticstability |