Continuous time Markov processes: an introduction
"Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes and applies this theory to various special examples. The initial chapter is devoted to the most important classical example--one-dimensi...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2010
|
| Schriftenreihe: | Graduate studies in mathematic
113 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Zusammenfassung: | "Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes and applies this theory to various special examples. The initial chapter is devoted to the most important classical example--one-dimensional Brownian motion. This, together with a chapter on continuous time Markov chains, provides the motivation for the general setup based on semigroups and generators. Chapters on stochastic calculus and probabilistic potential theory give an introduction to some of the key areas of application of Brownian motion and its relatives. A chapter on interacting particle systems treats a more recently developed class of Markov processes that have as their origin problems in physics and biology."--Publisher's description. |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XII, 271 S. graph. Darst. |
| ISBN: | 9780821849491 |
Internformat
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| 245 | 1 | 0 | |a Continuous time Markov processes |b an introduction |c Thomas M. Liggett |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2010 | |
| 300 | |a XII, 271 S. |b graph. Darst. | ||
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| 490 | 1 | |a Graduate studies in mathematics |v 113 | |
| 500 | |a Includes bibliographical references and index | ||
| 520 | 3 | |a "Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes and applies this theory to various special examples. The initial chapter is devoted to the most important classical example--one-dimensional Brownian motion. This, together with a chapter on continuous time Markov chains, provides the motivation for the general setup based on semigroups and generators. Chapters on stochastic calculus and probabilistic potential theory give an introduction to some of the key areas of application of Brownian motion and its relatives. A chapter on interacting particle systems treats a more recently developed class of Markov processes that have as their origin problems in physics and biology."--Publisher's description. | |
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Datensatz im Suchindex
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| adam_text | U
Xi
1б
Markov processes are among the most important stochastic
processes for both theory and applications. This book
develops the general theory of these processes and applies
this theory to various special examples. The initial chapter
is devoted to the most important classical example
—
one-
dimensional Brownian motion. This, together with a chapter
on continuous time Markov chains, provides the motivation
for the general setup based on semigroups and generators.
Chapters on stochastic calculus and probabilistic potential theory give an introduc¬
tion to some of the key areas of application of Brownian motion and its relatives.
A chapter on interacting particle systems treats a more recently developed class of
Markov processes that have as their origin problems in physics and biology.
This is a textbook for a graduate course that can follow one that covers basic
probabilistic limit theorems and discrete time processes.
Contents
Preface
ix
Chapter
1.
One-Dimensional Brownian Motion
1
§1.1.
Some motivation
1
§1.2.
The multivariate Gaussian distribution
2
§1.3.
Processes with stationary independent increments
5
§1.4.
Definition of Brownian motion
5
§1.5.
The construction
9
§1.6.
Path properties
15
§1.7.
The Markov property
21
§1.8.
The strong Markov property and applications
28
§1.9.
Continuous time martingales and applications
38
§1.10.
The Skorokhod embedding
47
§1.11.
Donsker s theorem and applications
51
Chapter
2.
Continuous Time Markov Chains
57
§2.1.
The basic setup
57
§2.2.
Some examples
59
§2.3.
From Markov chain to infinitesimal description
61
§2.4.
B lackwelľ s
example
65
§2.5.
From infinitesimal description to Markov chain
68
§2.6.
Stationary measures, recurrence, and transience
79
§2.7.
More examples
86
Chapter
3.
Feller Processes
91
§3.1.
The basic setup
91
§3.2.
From Feller process to infinitesimal description
98
§3.3.
From infinitesimal description to Feller process
102
§3.4.
A few tools
109
§3.5.
Applications to Brownian motion and its relatives
119
Chapter
4.
Interacting Particle Systems
133
§4.1.
Some motivation
133
§4.2.
Spin systems
134
§4.3.
The voter model
149
§4.4.
The contact process
161
§4.5.
Exclusion processes
175
Chapter
5.
Stochastic Integration
193
§5.1.
Some motivation
193
§5.2.
The
Ito
integral
195
§5.3.
Itô s
formula and applications
204
§5.4.
Brownian local time
213
§5.5.
Connections to Feller processes on R1
219
Chapter
6.
Multi-Dimensional Brownian Motion and the Dirichlet
Problem
227
§6.1.
Harmonic functions and the Dirichlet problem
228
§6.2.
Brownian motion on Rn
231
§6.3.
Back to the Dirichlet problem
237
§6.4.
The
Poisson
equation
245
Appendix
247
§A.l. Commonly used notation
247
§A.2. Some measure theory
248
§A.3. Some analysis
249
§A.4. The
Poisson
distribution
252
§A.5. Random series and laws of large numbers
252
§A.6. The central limit theorem and related topics
253
§A.7. Discrete time martingales
258
§A.8. Discrete time Markov chains
261
SA.
9.
The renewal theorem
263
§A.1O.
Harmonic functions for discrete time Markov chains
263
§A.ll.
Subadditive
functions
265
Bibliography
267
Index
269
|
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| author | Liggett, Thomas M. 1944-2020 |
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| classification_tum | MAT 607f |
| ctrlnum | (OCoLC)699830960 (DE-599)BSZ320504514 |
| dewey-full | 519.2/33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/33 |
| dewey-search | 519.2/33 |
| dewey-sort | 3519.2 233 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV036100861 |
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| indexdate | 2024-07-09T22:11:36Z |
| institution | BVB |
| isbn | 9780821849491 |
| language | English |
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| spelling | Liggett, Thomas M. 1944-2020 Verfasser (DE-588)10877869X aut Continuous time Markov processes an introduction Thomas M. Liggett Providence, RI American Math. Soc. 2010 XII, 271 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 113 Includes bibliographical references and index "Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes and applies this theory to various special examples. The initial chapter is devoted to the most important classical example--one-dimensional Brownian motion. This, together with a chapter on continuous time Markov chains, provides the motivation for the general setup based on semigroups and generators. Chapters on stochastic calculus and probabilistic potential theory give an introduction to some of the key areas of application of Brownian motion and its relatives. A chapter on interacting particle systems treats a more recently developed class of Markov processes that have as their origin problems in physics and biology."--Publisher's description. Markov processes Stochastic integrals Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 s Stochastisches Integral (DE-588)4126478-2 s DE-604 Graduate studies in mathematic 113 (DE-604)BV009739289 113 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018991229&sequence=000005&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018991229&sequence=000006&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Liggett, Thomas M. 1944-2020 Continuous time Markov processes an introduction Graduate studies in mathematic Markov processes Stochastic integrals Markov-Prozess (DE-588)4134948-9 gnd Stochastisches Integral (DE-588)4126478-2 gnd |
| subject_GND | (DE-588)4134948-9 (DE-588)4126478-2 |
| title | Continuous time Markov processes an introduction |
| title_auth | Continuous time Markov processes an introduction |
| title_exact_search | Continuous time Markov processes an introduction |
| title_full | Continuous time Markov processes an introduction Thomas M. Liggett |
| title_fullStr | Continuous time Markov processes an introduction Thomas M. Liggett |
| title_full_unstemmed | Continuous time Markov processes an introduction Thomas M. Liggett |
| title_short | Continuous time Markov processes |
| title_sort | continuous time markov processes an introduction |
| title_sub | an introduction |
| topic | Markov processes Stochastic integrals Markov-Prozess (DE-588)4134948-9 gnd Stochastisches Integral (DE-588)4126478-2 gnd |
| topic_facet | Markov processes Stochastic integrals Markov-Prozess Stochastisches Integral |
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