Essentials of Brownian motion and diffusion:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS
1981
|
| Series: | Mathematical surveys
18 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 201 S. |
| ISBN: | 0821815180 |
Staff View
MARC
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| 245 | 1 | 0 | |a Essentials of Brownian motion and diffusion |c by Frank B. Knight |
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Record in the Search Index
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| adam_text |
TABLE OF CONTENTS
Preface xi
Introduction 1
Chapter 1. Definition, Existence, and Uniqueness
of the Brownian Motion
1. The Basic Concept 5
2. Construction by Gaussian Interpolation 6
3. Construction as a Limit of Random Walks 9
4. Construction by Trigonometric Series 12
5. Uniqueness Questions and Notation 14
Chapter 2. Initial Features of the Process
1. Equivalence Transformations 19
2. Law of the Iterated Logarithm 22
3. Quadratic Variation 23
4. Modulus of Continuity 25
5. First Passage Times and Pointwise Recurrence 27
6. Hitting Probabilities (r = 1) 29
Chapter 3. General Markovian Methods
3.1. Analytic Methods 31
1. Brownian Transition Densities and Semigroups 31
2. General Markov Semigroups 33
3. Infinitesimal Generators 35
4. Brownian Generators and Resolvents 36
3.2. Probabilistic Methods 38
1. Markov Properties 39
2. Stopping Times and Strong Markov Properties 42
3. Zero or One Laws 50
4. Hitting Times and Dynkin's Formula 52
5. Foreseeability of Stopping Times 55
6. Additive Functionals 57
Chapter 4. Absorbing, Killing, and Time Changing:
The Classical Cases
4.1. Absorption 61
1. Two Absorbing Points 61
vii
Viii CONTENTS
2. Space-Time Process and the Heat Equation 63
3. The Dirichlet Problem in Rr 66
4. The Heat Equation in Rr 63
5. Moments of Passage Times 70
4.2. Killing 71
1. Killing at a Boundary 71
2. Killing by a Continuous Additive Functional 73
3. The Method of Kac and Rosenblatt 76
4. Some Sojourn Time Distributions 82
4.3. Time Changing 89
1. Sectionally Continuous Coefficients 90
2. The Corresponding Diffusions on (a, b) 91
3. The Ornstein-Uhlenbeck Velocity Process 96
4. Stochastic Differential Equations (Heuristic) 98
5. Continuous State Branching Processes 100
6. The Bessel Processes 102
7. Transience, Neighborhood Recurrence, and Passage Times 103
Chapter 5. Local Times, Excursions, and Absolute
Sample Path Properties
5.1. Local Time: Extrinsic Construction 107
1. The Skeletal Random Walk 107
2. The Limit Diffusion 1 \q
3. Trotter's Theorem and Local Time as a Family
of Additive Functionals 115
5.2. Brownian Excursions 120
1. The Brownian Flow 120
2. The Normalized Excursion 122
3. Probabilistic Structure of an Excursion 123
4. Distribution of the Maximum 125
5.3. The Zero Set and Intrinsic Local Time 127
1. Distribution of the Zeros 127
2. Construction of Process from Zeros and Excursions 128
3. P. Levy's Equivalence (Yx(t), M(t)) = {\B(i)\, 2s(t, 0)) 130
4. Passage Time Process as Subordinator 132
5. The "Mesure du Voisinage" and Local Time 135
6. The General Sojourn Density Diffusions 137
7. Local Times of Diffusions 139
5.4. Some Absolute Sample Path Properties 142
1. Upper and Lower Classes Locally 142
2. Lower Escape Rates 141
3. Global Upper and Lower Moduli 148
4. Measure of the Range (r 2) 149
CONTENTS ix
5. Total Path Variation (r = 1) 149
6. Absence of Differentiability or Times of Increase 150
Chapter 6. Boundary Conditions for Brownian Motion (r = 1)
1. Brownian Motions on [0, oo): Generators 153
2. Construction of the Processes 157
3. Brownian Motions on [0, 1] 162
4. Green Functions and Eigenfunction Expansions 163
Chapter 7. Nonsingular Diffusion in R'
7.1. The Deductive Approach 169
1. First Passage Times and Semigroups 170
2. Local Infinitesimal Generators 173
7.2. The Constructive Approach 176
7.3. Conservative Boundary Conditions 181
7.4. Nonconservative Diffusion 186
1. The General Continuous Additive Functional 187
2. The General Killed Diffusion 191
Bibliography 195
Index 199 |
| any_adam_object | 1 |
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| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV002140503 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-12T17:00:48Z |
| institution | BVB |
| isbn | 0821815180 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001403849 |
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| physical | XIII, 201 S. |
| psigel | TUB-nveb |
| publishDate | 1981 |
| publishDateSearch | 1981 |
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| publisher | AMS |
| record_format | marc |
| series | Mathematical surveys |
| series2 | Mathematical surveys |
| spelling | Knight, Frank B. 1933-2007 Verfasser (DE-588)171065948 aut Essentials of Brownian motion and diffusion by Frank B. Knight Providence, RI AMS 1981 XIII, 201 S. txt rdacontent n rdamedia nc rdacarrier Mathematical surveys 18 Matematica Aplicada larpcal Mouvement brownien, Processus de Processos Markovianos larpcal Processus de diffusion Brownian motion processes Diffusion processes Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Diffusionsprozess (DE-588)4274463-5 gnd rswk-swf Diffusionsprozess (DE-588)4274463-5 s DE-604 Brownsche Bewegung (DE-588)4128328-4 s Mathematical surveys 18 (DE-604)BV001888016 18 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001403849&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Knight, Frank B. 1933-2007 Essentials of Brownian motion and diffusion Mathematical surveys Matematica Aplicada larpcal Mouvement brownien, Processus de Processos Markovianos larpcal Processus de diffusion Brownian motion processes Diffusion processes Brownsche Bewegung (DE-588)4128328-4 gnd Diffusionsprozess (DE-588)4274463-5 gnd |
| subject_GND | (DE-588)4128328-4 (DE-588)4274463-5 |
| title | Essentials of Brownian motion and diffusion |
| title_auth | Essentials of Brownian motion and diffusion |
| title_exact_search | Essentials of Brownian motion and diffusion |
| title_full | Essentials of Brownian motion and diffusion by Frank B. Knight |
| title_fullStr | Essentials of Brownian motion and diffusion by Frank B. Knight |
| title_full_unstemmed | Essentials of Brownian motion and diffusion by Frank B. Knight |
| title_short | Essentials of Brownian motion and diffusion |
| title_sort | essentials of brownian motion and diffusion |
| topic | Matematica Aplicada larpcal Mouvement brownien, Processus de Processos Markovianos larpcal Processus de diffusion Brownian motion processes Diffusion processes Brownsche Bewegung (DE-588)4128328-4 gnd Diffusionsprozess (DE-588)4274463-5 gnd |
| topic_facet | Matematica Aplicada Mouvement brownien, Processus de Processos Markovianos Processus de diffusion Brownian motion processes Diffusion processes Brownsche Bewegung Diffusionsprozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001403849&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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