Introduction to the theory of random processes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
2002
|
| Series: | Graduate studies in mathematics
Volume 43 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 230 S. |
| ISBN: | 0821829858 9780821829851 |
Staff View
MARC
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| 100 | 1 | |a Krylov, Nikolaj V. |d 1941- |e Verfasser |0 (DE-588)121699684 |4 aut | |
| 245 | 1 | 0 | |a Introduction to the theory of random processes |c N. V. Krylov |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2002 | |
| 300 | |a XII, 230 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v Volume 43 | |
| 650 | 7 | |a PROCESSOS ESTOCASTICOS |2 larpcal | |
| 650 | 4 | |a Processus stochastiques | |
| 650 | 4 | |a Stochastic processes | |
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Record in the Search Index
| _version_ | 1804129064488796160 |
|---|---|
| adam_text | Contents
Preface
xi
Chapter
1.
Generalities
. 1
§1.
Some selected topics from probability theory
1
§2.
Some facts from measure theory on Polish spaces
5
§3.
The notion of random process
14
§4.
Continuous random processes
16
§5.
Hints to exercises
25
Chapter
2.
The Wiener Process
27
§1.
Brownian motion and the Wiener process
27
§2.
Some properties of the Wiener process
32
§3.
Integration against random orthogonal measures
39
§4.
The Wiener process on
[0,
oo)
50
§5.
Markov and strong Markov properties of the Wiener process
52
§6.
Examples of applying the strong Markov property
57
§7.
Ito
stochastic integral
61
§8.
The structure of
Ito
integrable
functions
65
§9.
Hints to exercises
69
Chapter
3.
Martingales
71
vii
viii Contents
§1.
Conditional expectations
71
§2.
Discrete time martingales
78
§3.
Properties of martingales
81
§4.
Limit theorems for martingales
87
§5.
Hints to exercises
92
Chapter
4.
Stationary Processes
95
§1.
Simplest properties of second-order stationary processes
95
§2.
Spectral decomposition of trajectories
101
§3.
Ornstein-Uhlenbeck process
105
§4.
Gaussian stationary processes with rational spectral densities
112
§5.
Remarks about predicting Gaussian stationary
processes with rational spectral densities
117
§6.
Stationary processes and the Birkhoff-Khinchin theorem
119
§7.
Hints to exercises
127
Chapter
5.
Infinitely Divisible Processes
131
§1.
Stochastically continuous processes with independent increments
131
§2.
Lévy-Khinchin
theorem
137
§3.
Jump measures and their relation to Levy measures
144
§4.
Further comments on jump measures
154
§5.
Representing infinitely divisible processes through jump measures
155
§6.
Constructing infinitely divisible processes
160
§7.
Hints to exercises
166
Chapter
6.
Ito
Stochastic Integral
169
§1.
The classical definition
169
§2.
Properties of the stochastic integral on
H
174
§3.
Defining the
Ito
integral if f£
ƒƒ
ds
<
oo
179
§4.
Ito
integral with respect to a multidimensional Wiener process
186
§5.
Itô s
formula
188
§6.
An alternative proof of
Itô s
formula
195
Contents ix
§7.
Examples of applying
Itô s
formula
200
§8.
Girsanov s theorem
204
§9.
Stochastic
Ito
equations
211
§10.
An example of a stochastic equation
216
§11.
The Markov property of solutions of stochastic equations
220
§12.
Hints to exercises
225
Bibliography
227
Index
229
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/3 |
| dewey-search | 519.2/3 |
| dewey-sort | 3519.2 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014185970 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:59:12Z |
| institution | BVB |
| isbn | 0821829858 9780821829851 |
| language | English |
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| physical | XII, 230 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Krylov, Nikolaj V. 1941- Verfasser (DE-588)121699684 aut Introduction to the theory of random processes N. V. Krylov Providence, RI American Mathematical Society 2002 XII, 230 S. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics Volume 43 PROCESSOS ESTOCASTICOS 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 978-1-4704-2094-9 Graduate studies in mathematics Volume 43 (DE-604)BV009739289 43 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009723667&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krylov, Nikolaj V. 1941- Introduction to the theory of random processes Graduate studies in mathematics PROCESSOS ESTOCASTICOS larpcal Processus stochastiques Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 |
| title | Introduction to the theory of random processes |
| title_auth | Introduction to the theory of random processes |
| title_exact_search | Introduction to the theory of random processes |
| title_full | Introduction to the theory of random processes N. V. Krylov |
| title_fullStr | Introduction to the theory of random processes N. V. Krylov |
| title_full_unstemmed | Introduction to the theory of random processes N. V. Krylov |
| title_short | Introduction to the theory of random processes |
| title_sort | introduction to the theory of random processes |
| topic | PROCESSOS ESTOCASTICOS larpcal Processus stochastiques Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | PROCESSOS ESTOCASTICOS Processus stochastiques Stochastic processes Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009723667&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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