Stochastic processes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Courant Inst. of Math. Sciences [u.a.]
2007
|
| Series: | Courant lecture notes in mathematics
16 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | IX, 126 S. |
| ISBN: | 9780821840856 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
ix
Chapter
1.
Introduction
1
1.1.
Continuous Time Processes
1
1.2.
Continuous Parameter Martingales
3
1.3.
Semimartingales
8
1.4.
Martingales and Stochastic Integrals
10
Chapter
2.
Processes with Independent Increments
13
2.1.
The Basic
Poisson
Process
13
2.2.
Compound
Poisson
Processes
16
2.3.
Infinite Number of Small Jumps
17
2.4.
Infinitesimal Generators
20
2.5.
Some Associated Martingales
21
Chapter
3.
Poisson
Point Processes
25
3.1.
Point Processes
25
3.2.
Poisson
Point Process
26
Chapter
4.
Jump Markov Processes
29
4.1.
Simple Examples
29
4.2.
Semigroups of Operators
31
4.3.
Example: Birth and Death Processes
34
4.4.
Markov Processes and Martingales
35
4.5.
Explosion
39
4.6.
Recurrence and Transience
44
4.7.
Invariant Distributions
45
4.8.
Beyond Explosion
47
Chapter
5.
Brownian Motion
49
5.1.
Definition of Brownian Motion
49
5.2.
Markov and Strong Markov Property
51
5.3.
Heat Equation
53
5.4.
Recurrence
55
5.5.
Feynman-Kac Formula
56
5.6.
Arcsine Law
57
5.7.
Harmonic Oscillator
59
5.8.
Exit Times from Bounded Intervals
60
viü CONTENTS
5.9.
Stochastic Integrals
61
5.10.
Brownian Motion with a Drift, Girsanov Formula
69
5.11.
Ornstein-Uhlenbeck Process
72
5.12.
Invariant Densities
75
5.13.
Local Times
76
5.14.
Reflected Brownian Motion
79
5.15.
Excursion Theory
81
5.16.
Invariance
Principle
83
5.17.
Representation of Martingales
85
Chapter
6.
One-Dimensional Diffusions
87
6.1.
Stochastic Differential Equations
87
6.2.
Properties of the Solution
90
6.3.
Connections with Differential Equations
94
6.4.
Martingale Characterization
97
6.5.
Random Time Change
99
6.6.
Some Examples
100
Chapter
7.
General Theory of Markov Processes
107
7.1.
Introduction
107
7.2.
Semigroups, Generators and Resolvents
108
7.3.
Generators and Martingales
110
7.4.
Invariant Measures and Ergodic Theory
111
Appendix A. Measures on Polish Spaces
113
A.I. The Space C[0,
1] 116
A.2. The Space D[0,
1] 118
Appendix B. Additional Remarks
121
Bibliography
123
Index
125
This is a brief introduction to stochastic processes studying certain
elementary continuous-time processes. After a description of the
Poisson
process and related processes with independent increments as well as a
brief look at Markov processes with a finite number of jumps, the author
proceeds to introduce Brownian motion and to develop stochastic integrals
and Ito s theory in the context of one-dimensional diffusion processes. The
book ends with a brief survey of the general theory of Markov processes.
The book is based on courses given by the author at the
Courant
Institute
and can be used as a sequel to the author s successful book Probability
in this series.
|
| adam_txt |
Contents
Preface
ix
Chapter
1.
Introduction
1
1.1.
Continuous Time Processes
1
1.2.
Continuous Parameter Martingales
3
1.3.
Semimartingales
8
1.4.
Martingales and Stochastic Integrals
10
Chapter
2.
Processes with Independent Increments
13
2.1.
The Basic
Poisson
Process
13
2.2.
Compound
Poisson
Processes
16
2.3.
Infinite Number of Small Jumps
17
2.4.
Infinitesimal Generators
20
2.5.
Some Associated Martingales
21
Chapter
3.
Poisson
Point Processes
25
3.1.
Point Processes
25
3.2.
Poisson
Point Process
26
Chapter
4.
Jump Markov Processes
29
4.1.
Simple Examples
29
4.2.
Semigroups of Operators
31
4.3.
Example: Birth and Death Processes
34
4.4.
Markov Processes and Martingales
35
4.5.
Explosion
39
4.6.
Recurrence and Transience
44
4.7.
Invariant Distributions
45
4.8.
Beyond Explosion
47
Chapter
5.
Brownian Motion
49
5.1.
Definition of Brownian Motion
49
5.2.
Markov and Strong Markov Property
51
5.3.
Heat Equation
53
5.4.
Recurrence
55
5.5.
Feynman-Kac Formula
56
5.6.
Arcsine Law
57
5.7.
Harmonic Oscillator
59
5.8.
Exit Times from Bounded Intervals
60
viü CONTENTS
5.9.
Stochastic Integrals
61
5.10.
Brownian Motion with a Drift, Girsanov Formula
69
5.11.
Ornstein-Uhlenbeck Process
72
5.12.
Invariant Densities
75
5.13.
Local Times
76
5.14.
Reflected Brownian Motion
79
5.15.
Excursion Theory
81
5.16.
Invariance
Principle
83
5.17.
Representation of Martingales
85
Chapter
6.
One-Dimensional Diffusions
87
6.1.
Stochastic Differential Equations
87
6.2.
Properties of the Solution
90
6.3.
Connections with Differential Equations
94
6.4.
Martingale Characterization
97
6.5.
Random Time Change
99
6.6.
Some Examples
100
Chapter
7.
General Theory of Markov Processes
107
7.1.
Introduction
107
7.2.
Semigroups, Generators and Resolvents
108
7.3.
Generators and Martingales
110
7.4.
Invariant Measures and Ergodic Theory
111
Appendix A. Measures on Polish Spaces
113
A.I. The Space C[0,
1] 116
A.2. The Space D[0,
1] 118
Appendix B. Additional Remarks
121
Bibliography
123
Index
125
This is a brief introduction to stochastic processes studying certain
elementary continuous-time processes. After a description of the
Poisson
process and related processes with independent increments as well as a
brief look at Markov processes with a finite number of jumps, the author
proceeds to introduce Brownian motion and to develop stochastic integrals
and Ito\s theory in the context of one-dimensional diffusion processes. The
book ends with a brief survey of the general theory of Markov processes.
The book is based on courses given by the author at the
Courant
Institute
and can be used as a sequel to the author's successful book Probability
in this series. |
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| id | DE-604.BV023022400 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:13:39Z |
| indexdate | 2024-07-09T21:09:11Z |
| institution | BVB |
| isbn | 9780821840856 |
| language | English |
| lccn | 2007060837 |
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| physical | IX, 126 S. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Courant Inst. of Math. Sciences [u.a.] |
| record_format | marc |
| series | Courant lecture notes in mathematics |
| series2 | Courant lecture notes in mathematics |
| spelling | Varadhan, S. R. S. 1940- Verfasser (DE-588)13051957X aut Stochastic processes S. R. S. Varadhan New York, NY Courant Inst. of Math. Sciences [u.a.] 2007 IX, 126 S. txt rdacontent n rdamedia nc rdacarrier Courant lecture notes in mathematics 16 Processos estocásticos larpcal Processus stochastiques Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-3116-7 Courant lecture notes in mathematics 16 (DE-604)BV012714106 16 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016226434&sequence=000002&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=016226434&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Varadhan, S. R. S. 1940- Stochastic processes Courant lecture notes in mathematics Processos estocásticos larpcal Processus stochastiques Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 |
| title | Stochastic processes |
| title_auth | Stochastic processes |
| title_exact_search | Stochastic processes |
| title_exact_search_txtP | Stochastic processes |
| title_full | Stochastic processes S. R. S. Varadhan |
| title_fullStr | Stochastic processes S. R. S. Varadhan |
| title_full_unstemmed | Stochastic processes S. R. S. Varadhan |
| title_short | Stochastic processes |
| title_sort | stochastic processes |
| topic | Processos estocásticos larpcal Processus stochastiques Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Processos estocásticos Processus stochastiques Stochastic processes Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016226434&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016226434&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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