Handbook of Brownian motion: facts and formulae
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
1996
|
| Series: | Probability and its applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 462 S. |
| ISBN: | 3764354631 0817654631 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | ANDREI N
. BORODIN
PAAVO SALMINEN
HANDBOOK OF
BROWNIAN MOTION -
FACTS AND FORMULAE
BIRKHAUSER VERLAG
BASEL YY BOSTON YY BERLIN
CONTENTS
PREFACE XI
NOTATION
XIII
PAR
T
I:
THEORY
CHAPTE
R I. STOCHASTI
C PROCESSE
S IN GENERA
L
1. BASIC DEFINITIONS 1
2. MARKOV PROCESSES, TRANSITION FUNCTIONS, RESOLVENTS, AND GENERATORS 3
3. FELLER PROCESSES, FELLER-DYNKIN PROCESSES, AND
THE STRONG MARKOV PROPERTY 5
4. MARTINGALES 7
CHAPTE
R II
. LINEAR DIFFUSIONS
1. BASIC FACTS 12
2. LOCAL TIME 20
3. PASSAGE TIMES 24
4. ADDITIVE FUNCTIONALS AND KILLING 27
5. EXCESSIVE FUNCTIONS 31
6. ERGODIC RESULTS 34
CHAPTER III. STOCHASTIC CALCULUS
1.
STOCHASTIC INTEGRATION WITH RESPECT TO BROWNIAN MOTION 37
2. THE ITO AND TANAKA FORMULAE 40
3. THE CAMERON-MARTIN-GIRSANOV TRANSFORMATION OF MEASURE 42
4. STOCHASTIC DIFFERENTIAL EQUATIONS - STRONG SOLUTIONS 44
5. STOCHASTIC DIFFERENTIAL EQUATIONS - WEAK SOLUTIONS 45
6. ONE-DIMENSIONAL STOCHASTIC DIFFERENTIAL EQUATIONS 46
CHAPTE
R IV
. BROWNIA
N MOTIO
N
1. DEFINITION AND BASIC PROPERTIES 48
2. BROWNIAN LOCAL TIME 51
3. EXCURSIONS 53
4. BROWNIAN BRIDGE 60
5. BROWNIAN MOTION WITH DRIFT 63
6. BESSEL PROCESSES 66
VIII CONTENTS
CHAPTE
R V
. LOCAL TIM
E AS A MARKOV PROCES
S
1. DIFFUSION LOCAL TIME 71
2. LOCAL TIME OF BROWNIAN MOTION 74
2. LOCAL TIME OF BROWNIAN MOTION WITH DRIFT 78
4. LOCAL TIME OF BESSEL PROCESS 83
CHAPTER VI
. DIFFERENTIAL SYSTEM
S ASSOCIATE
D T
O BROWNIA
N MOTIO
N
1. THE FEYNMAN-KAC FORMULA 88
2. EXPONENTIAL STOPPING 90
3. STOPPING AT FIRST EXIT TIME 94
4. STOPPING AT INVERSE ADDITIVE FUNCTIONAL 97
APPENDI
X 1. BRIEFLY O
N SOM
E DIFFUSIONS
102
PAR
T II: TABLES OF DISTRIBUTIONS OF FUNCTIONALS
OF BROWNIAN MOTION AND RELATED PROCESSES
INTRODUCTIO
N
1. LIST OF FUNCTIONALS 121
2. COMMENTS AND REFERENCES 123
1. BROWNIA
N MOTIO
N
1.
EXPONENTIAL STOPPING 125
2. STOPPING AT FIRST HITTING TIME 163
3. STOPPING AT FIRST EXIT TIME 172
4. STOPPING AT INVERSE LOCAL TIME 185
2. BROWNIAN MOTIO
N WIT
H DRIFT
1. EXPONENTIAL STOPPING 197
2. STOPPING AT FIRST HITTING TIME 223
3. STOPPING AT FIRST EXIT TIME 233
4. STOPPING AT INVERSE LOCAL TIME 242
3
. REFLECTIN
G BROWNIA
N MOTIO
N
1. EXPONENTIAL STOPPING 250
2. STOPPING AT FIRST HITTING TIME 265
4. STOPPING AT INVERSE LOCAL TIME 272
4
. BESSE
L PROCES
S OF ORDER ZERO
1. EXPONENTIAL STOPPING 280
2. STOPPING AT FIRST HITTING TIME 297
3. STOPPING AT FIRST EXIT TIME 302
4. STOPPING AT INVERSE LOCAL TIME 311
CONTENTS IX
5. BESSE
L PROCESS OF ORDER 1/
2
1. EXPONENTIAL STOPPING 317
2. STOPPING AT FIRST HITTING TIME 339
3. STOPPING AT FIRST EXIT TIME 348
4. STOPPING AT INVERSE LOCAL TIME 358
6. BESSE
L PROCES
S OF ORDER
V
0
1. EXPONENTIAL STOPPING 369
2. STOPPING AT FIRST HITTING TIME 387
3. STOPPING AT FIRST EXIT TIME 394
4. STOPPING AT INVERSE LOCAL TIME 404
7. ORNSTEIN-UHLENBECK PROCES
S
1. EXPONENTIAL STOPPING 412
2. STOPPING AT FIRST HITTING TIME 429
3. STOPPING AT FIRST EXIT TIME 434
4. STOPPING AT INVERSE LOCAL TIME 442
APPENDI
X 2. SPECIAL FUNCTIONS
449
BIBLIOGRAPHY
454
SUBJECT INDE
X 460
|
| any_adam_object | 1 |
| author | Borodin, Andrej N. 1953- Salminen, Paavo 1951- |
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| ctrlnum | (OCoLC)845239089 (DE-599)BVBBV010896948 |
| 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 | Physik Mathematik |
| format | Book |
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| indexdate | 2024-07-09T18:00:45Z |
| institution | BVB |
| isbn | 3764354631 0817654631 |
| language | English |
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| physical | XIV, 462 S. |
| publishDate | 1996 |
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| series2 | Probability and its applications |
| spelling | Borodin, Andrej N. 1953- Verfasser (DE-588)12470218X aut Handbook of Brownian motion facts and formulae Andrei N. Borodin ; Paavo Salminen Basel [u.a.] Birkhäuser 1996 XIV, 462 S. txt rdacontent n rdamedia nc rdacarrier Probability and its applications Brownse beweging gtt Mouvement brownien, Processus de ram Brownian motion processes Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf (DE-588)4155008-0 Formelsammlung gnd-content Brownsche Bewegung (DE-588)4128328-4 s DE-604 Salminen, Paavo 1951- Verfasser (DE-588)1055794565 aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007287745&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Borodin, Andrej N. 1953- Salminen, Paavo 1951- Handbook of Brownian motion facts and formulae Brownse beweging gtt Mouvement brownien, Processus de ram Brownian motion processes Brownsche Bewegung (DE-588)4128328-4 gnd |
| subject_GND | (DE-588)4128328-4 (DE-588)4155008-0 |
| title | Handbook of Brownian motion facts and formulae |
| title_auth | Handbook of Brownian motion facts and formulae |
| title_exact_search | Handbook of Brownian motion facts and formulae |
| title_full | Handbook of Brownian motion facts and formulae Andrei N. Borodin ; Paavo Salminen |
| title_fullStr | Handbook of Brownian motion facts and formulae Andrei N. Borodin ; Paavo Salminen |
| title_full_unstemmed | Handbook of Brownian motion facts and formulae Andrei N. Borodin ; Paavo Salminen |
| title_short | Handbook of Brownian motion |
| title_sort | handbook of brownian motion facts and formulae |
| title_sub | facts and formulae |
| topic | Brownse beweging gtt Mouvement brownien, Processus de ram Brownian motion processes Brownsche Bewegung (DE-588)4128328-4 gnd |
| topic_facet | Brownse beweging Mouvement brownien, Processus de Brownian motion processes Brownsche Bewegung Formelsammlung |
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