Markov processes: characterization and convergence
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2005
|
| Edition: | [Nachdruck] |
| Series: | Wiley series in probability and mathematical statistics
|
| Subjects: | |
| Online Access: | Beschreibung für Leser Inhaltsverzeichnis |
| Physical Description: | X, 534 Seiten |
| ISBN: | 9780471769866 047176986X |
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MARC
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Record in the Search Index
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| adam_text |
CONTENTS
Introduction
1 Operator
Semigroups
1
Definitions and Basic Properties,
б
2
The Hille-Yosida Theorem,
10
3
Cores,
16
4
Multivalued Operators,
20
5
Semigroups on Function Spaces,
22
6
Approximation Theorems,
28
7
Perturbation Theorems,
37
8
Problems,
42
9
Notes,
47
2
Stochastic Processes and Martingales
49
1
Stochastic Processes,
49
2
Martingales,
55
3
Local Martingales,
64
4
The Projection Theorem,
71
5
The Doob-Meyer Decomposition,
74
6
Square
Integrable
Martingales,
78
7
Semigroups of Conditioned Shifts,
80
8
Martingales Indexed by Directed Sets,
84
9
Problems,
89
10
Notes,
93
vii
viii CONTENTS
3
Convergence of Probability Measures
95
1
The Prohorov Metric,
96
2
Prohorov's Theorem,
103
3
Weak Convergence,
107
4
Separating and Convergence Determining Sets,
111
5
The Space DEi0, oo),
116
6
The Compact Sets of O£[0, oo),
122
7
Convergence in Distribution in
DE[0,
oo),
127
8
Criteria for Relative Compactness in DE[0, oo),
132
9
Further Criteria for Relative Compactness
inD£[0, oo),
141
10
Convergence to a Process in Cc[0, oo),
147
11
Problems,
150
12
Notes,
154
4
Generators and Markov Processes
155
1
Markov Processes and Transition Functions,
156
2
Markov Jump Processes and Feller Processes,
162
3
The Martingale Problem: Generalities and Sample
Path Properties,
173
4
The Martingale Problem: Uniqueness, the Markov
Property, and Duality,
182
5
The Martingale Problem: Existence,
196
6
The Martingale Problem: Localization,
216
7
The Martingale Problem: Generalizations,
221
8
Convergence Theorems,
225
9
Stationary Distributions,
238
10
Perturbation Results,
253
11 Problems,
261
12
Notes,
273
5
Stochastic integral Equations
275
1
Brownian Motion,
275
2
Stochastic Integrals,
279
3
Stochastic Integral Equations,
290
4
Problems,
302
5
Notes,
305
6
Random Time Changes
306
1
One-Parameter Random Time Changes,
306
2
Mul t
¡parameter Random Time Changes,
311
3
Convergence,
321
CONTiNTS
¡Ж
4
Markov Processes in Z",
329
5
Diffusion Processes,
328
6
Problems,
332
7
Notes,
335
7
Invariance
Principles and Diffusion Approximations
337
1
The Martingale Central Limit Theorem,
338
2
Measures of Mixing, 34S
3
Central Limit Theorems for Stationary Sequences, 3S0
4
Diffusion Approximations,
354
5
Strong Approximation Theorems,
356
6
Problems,
360
7
Notes,
364
8
Examples of Generators
365
1
Nondegenerate
Diffusions,
366
2
Degenerate Diffusions,
371
3
Other Processes,
376
4
Problems,
382
5
Notes,
385
9
Branching Processes
386
1
Galton-Watson Processes,
386
2
Two-Type Markov Branching Processes,
392
3
Branching Processes in Random Environments,
396
4
Branching Markov Processes,
400
5
Problems,
407
6
Notes,
409
10
Genetic Models
410
1 The Wright-Fisher Model,
411
2
Applications of the Diffusion Approximation,
415
3
Genotypic-Frequency Models,
426
4
Infinitely-Many-Allele Models,
435
5
Problems,
448
6
Notes,
451
11
Density Dependent Population Processes
452
1
Examples,
452
2
Law of Large Numbers and Central Limit Theorem,
455
X
CONTENTS
3
Diffusion Approximations,
459
4
Hitting Distributions,
464
5
Problems,
466
6
Notes,
467
12
Random Evolutions
468
1
Introduction,
468
2
Driving Process in a Compact State Space,
472
3
Driving Process in a Noncompact State Space,
479
4
Non-Markovian Driving Process,
483
5
Problems,
491
6
Notes,
491
Appendixes
492
1
Convergence or Expectations,
492
2
Uniform Integrability,
493
3
Bounded Pointwise Convergence, 49S
4
Monotone Class Theorems,
496
5
Gronwall's Inequality,
498
6
The Whitney Extension Theorem,
499
7
Approximation by Polynomials,
500
8
Bimeasures and Transition Functions,
502
9
Tulcea's Theorem,
504
10
Measurable Selections and Measurability of Inverses,
506
11
Analytic Sets,
506
References
508
Index
521
Flowchart
529 |
| adam_txt |
CONTENTS
Introduction
1 Operator
Semigroups
1
Definitions and Basic Properties,
б
2
The Hille-Yosida Theorem,
10
3
Cores,
16
4
Multivalued Operators,
20
5
Semigroups on Function Spaces,
22
6
Approximation Theorems,
28
7
Perturbation Theorems,
37
8
Problems,
42
9
Notes,
47
2
Stochastic Processes and Martingales
49
1
Stochastic Processes,
49
2
Martingales,
55
3
Local Martingales,
64
4
The Projection Theorem,
71
5
The Doob-Meyer Decomposition,
74
6
Square
Integrable
Martingales,
78
7
Semigroups of Conditioned Shifts,
80
8
Martingales Indexed by Directed Sets,
84
9
Problems,
89
10
Notes,
93
vii
viii CONTENTS
3
Convergence of Probability Measures
95
1
The Prohorov Metric,
96
2
Prohorov's Theorem,
103
3
Weak Convergence,
107
4
Separating and Convergence Determining Sets,
111
5
The Space DEi0, oo),
116
6
The Compact Sets of O£[0, oo),
122
7
Convergence in Distribution in
DE[0,
oo),
127
8
Criteria for Relative Compactness in DE[0, oo),
132
9
Further Criteria for Relative Compactness
inD£[0, oo),
141
10
Convergence to a Process in Cc[0, oo),
147
11
Problems,
150
12
Notes,
154
4
Generators and Markov Processes
155
1
Markov Processes and Transition Functions,
156
2
Markov Jump Processes and Feller Processes,
162
3
The Martingale Problem: Generalities and Sample
Path Properties,
173
4
The Martingale Problem: Uniqueness, the Markov
Property, and Duality,
182
5
The Martingale Problem: Existence,
196
6
The Martingale Problem: Localization,
216
7
The Martingale Problem: Generalizations,
221
8
Convergence Theorems,
225
9
Stationary Distributions,
238
10
Perturbation Results,
253
11 Problems,
261
12
Notes,
273
5
Stochastic integral Equations
275
1
Brownian Motion,
275
2
Stochastic Integrals,
279
3
Stochastic Integral Equations,
290
4
Problems,
302
5
Notes,
305
6
Random Time Changes
306
1
One-Parameter Random Time Changes,
306
2
Mul t
¡parameter Random Time Changes,
311
3
Convergence,
321
CONTiNTS
¡Ж
4
Markov Processes in Z",
329
5
Diffusion Processes,
328
6
Problems,
332
7
Notes,
335
7
Invariance
Principles and Diffusion Approximations
337
1
The Martingale Central Limit Theorem,
338
2
Measures of Mixing, 34S
3
Central Limit Theorems for Stationary Sequences, 3S0
4
Diffusion Approximations,
354
5
Strong Approximation Theorems,
356
6
Problems,
360
7
Notes,
364
8
Examples of Generators
365
1
Nondegenerate
Diffusions,
366
2
Degenerate Diffusions,
371
3
Other Processes,
376
4
Problems,
382
5
Notes,
385
9
Branching Processes
386
1
Galton-Watson Processes,
386
2
Two-Type Markov Branching Processes,
392
3
Branching Processes in Random Environments,
396
4
Branching Markov Processes,
400
5
Problems,
407
6
Notes,
409
10
Genetic Models
410
1 The Wright-Fisher Model,
411
2
Applications of the Diffusion Approximation,
415
3
Genotypic-Frequency Models,
426
4
Infinitely-Many-Allele Models,
435
5
Problems,
448
6
Notes,
451
11
Density Dependent Population Processes
452
1
Examples,
452
2
Law of Large Numbers and Central Limit Theorem,
455
X
CONTENTS
3
Diffusion Approximations,
459
4
Hitting Distributions,
464
5
Problems,
466
6
Notes,
467
12
Random Evolutions
468
1
Introduction,
468
2
Driving Process in a Compact State Space,
472
3
Driving Process in a Noncompact State Space,
479
4
Non-Markovian Driving Process,
483
5
Problems,
491
6
Notes,
491
Appendixes
492
1
Convergence or Expectations,
492
2
Uniform Integrability,
493
3
Bounded Pointwise Convergence, 49S
4
Monotone Class Theorems,
496
5
Gronwall's Inequality,
498
6
The Whitney Extension Theorem,
499
7
Approximation by Polynomials,
500
8
Bimeasures and Transition Functions,
502
9
Tulcea's Theorem,
504
10
Measurable Selections and Measurability of Inverses,
506
11
Analytic Sets,
506
References
508
Index
521
Flowchart
529 |
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| id | DE-604.BV023217306 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T20:14:35Z |
| indexdate | 2024-07-20T05:15:59Z |
| institution | BVB |
| isbn | 9780471769866 047176986X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016403268 |
| oclc_num | 62724166 |
| open_access_boolean | |
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| physical | X, 534 Seiten |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and mathematical statistics |
| spelling | Ethier, Stewart N. 1948- Verfasser (DE-588)141523905 aut Markov processes characterization and convergence Stewart N. Ethier and Thomas G. Kurtz [Nachdruck] Hoboken, NJ Wiley 2005 X, 534 Seiten txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics Processos de markov larpcal Markov processes Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 s DE-604 Kurtz, Thomas G. 1941- Verfasser (DE-588)129841714 aut Erscheint auch als Online-Ausgabe 978-0-470-31665-8 http://deposit.dnb.de/cgi-bin/dokserv?id=2775193&prov=M&dok_var=1&dok_ext=htm Beschreibung für Leser Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016403268&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ethier, Stewart N. 1948- Kurtz, Thomas G. 1941- Markov processes characterization and convergence Processos de markov larpcal Markov processes Markov-Prozess (DE-588)4134948-9 gnd |
| subject_GND | (DE-588)4134948-9 |
| title | Markov processes characterization and convergence |
| title_auth | Markov processes characterization and convergence |
| title_exact_search | Markov processes characterization and convergence |
| title_exact_search_txtP | Markov processes characterization and convergence |
| title_full | Markov processes characterization and convergence Stewart N. Ethier and Thomas G. Kurtz |
| title_fullStr | Markov processes characterization and convergence Stewart N. Ethier and Thomas G. Kurtz |
| title_full_unstemmed | Markov processes characterization and convergence Stewart N. Ethier and Thomas G. Kurtz |
| title_short | Markov processes |
| title_sort | markov processes characterization and convergence |
| title_sub | characterization and convergence |
| topic | Processos de markov larpcal Markov processes Markov-Prozess (DE-588)4134948-9 gnd |
| topic_facet | Processos de markov Markov processes Markov-Prozess |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2775193&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=016403268&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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