Introduction to stochastic integration:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston ; Basel ; Berlin
Birkhäuser
1990
|
| Edition: | second edition |
| Series: | Probability and its applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xv, 276 Seiten Diagramme |
| ISBN: | 0817633863 3764333863 |
Staff View
MARC
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| 100 | 1 | |a Chung, Kai Lai |d 1917-2009 |0 (DE-588)136125484 |4 aut | |
| 245 | 1 | 0 | |a Introduction to stochastic integration |c K. L. Chung ; R. J. Williams |
| 250 | |a second edition | ||
| 264 | 1 | |a Boston ; Basel ; Berlin |b Birkhäuser |c 1990 | |
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Record in the Search Index
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|---|---|
| adam_text | TABLE OF CONTENTS
PREFACE v
PREFACE TO THE FIRST EDITION vii
ABBREVIATIONS AND SYMBOLS xiii
1. PRELIMINARIES 1
1.1 Notations and Conventions 1
1.2 Measurability, Lp Spaces and Monotone Class Theorems 2
1.3 Functions of Bounded Variation and Stieltjes Integrals 4
1.4 Probability Space, Random Variables, Filtration 6
1.5 Convergence, Conditioning 7
1.6 Stochastic Processes 8
1.7 Optional Times 9
1.8 Two Canonical Processes 10
1.9 Martingales 13
1.10 Local Martingales 18
1.11 Exercises 21
x TABLE OF CONTENTS
2. DEFINITION OF THE STOCHASTIC INTEGRAL 23
2.1 Introduction 23
2.2 Predictable Sets and Processes 25
2.3 Stochastic Intervals 26
2.4 Measure on the Predictable Sets 32
2.5 Definition of the Stochastic Integral 34
2.6 Extension to Local Integrators and Integrands 43
2.7 Substitution Formula 48
2.8 A Sufficient Condition for Extendability of z 50
2.9 Exercises 54
3. EXTENSION OF THE PREDICTABLE INTEGRANDS 57
3.1 Introduction 57
3.2 Relationship between V, O, and Adapted Processes 57
3.3 Extension of the Integrands 63
3.4 A Historical Note 71
3.5 Exercises 73
4. QUADRATIC VARIATION PROCESS 75
4.1 Introduction 75
4.2 Definition and Characterization of Quadratic Variation 75
4.3 Properties of Quadratic Variation for an £2 martingale 79
4.4 Direct Definition of hm 82
4.5 Decomposition of (M)2 86
4.6 A Limit Theorem 89
4.7 Exercises 90
5. THE ITO FORMULA 93
5.1 Introduction 93
5.2 One dimensional Ito Formula 94
5.3 Mutual Variation Process 99
5.4 Multi dimensional Ito Formula 109
5.5 Exercises 112
TABLE OF CONTENTS xi
6. APPLICATIONS OF THE ITO FORMULA 117
6.1 Characterization of Brownian Motion 117
6.2 Exponential Processes 120
6.3 A Family of Martingales Generated by M 123
6.4 Feynman Kac Functional and the Schrodinger Equation 128
6.5 Exercises 136
7. LOCAL TIME AND TANAKA S FORMULA 141
7.1 Introduction 141
7.2 Local Time 142
7.3 Tanaka s Formula 150
7.4 Proof of Lemma 7.2 153
7.5 Exercises 155
8. REFLECTED BROWNIAN MOTIONS 157
8.1 Introduction 157
8.2 Brownian Motion Reflected at Zero 158
8.3 Analytical Theory of Z via the Ito Formula 161
8.4 Approximations in Storage Theory 163
8.5 Reflected Brownian Motions in a Wedge 174
8.6 Alternative Derivation of Equation (8.7) 178
8.7 Exercises 181
9. GENERALIZED ITO FORMULA,
CHANGE OF TIME AND MEASURE 183
9.1 Introduction 183
9.2 Generalized Ito Formula 184
9.3 Change of Time 187
9.4 Change of Measure 197
9.5 Exercises 214
xii TABLE OF CONTENTS
10. STOCHASTIC DIFFERENTIAL EQUATIONS 217
10.1 Introduction 217
10.2 Existence and Uniqueness for Lipschitz Coefficients 220
10.3 Strong Markov Property of the Solution 235
10.4 Strong and Weak Solutions 243
10.5 Examples 252
10.6 Exercises 262
REFERENCES 265
INDEX 273
|
| any_adam_object | 1 |
| author | Chung, Kai Lai 1917-2009 Williams, Ruth J. 1955- |
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| dewey-search | 519.2 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | second edition |
| format | Book |
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| institution | BVB |
| isbn | 0817633863 3764333863 |
| language | English |
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| physical | xv, 276 Seiten Diagramme |
| publishDate | 1990 |
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| series2 | Probability and its applications |
| spelling | Chung, Kai Lai 1917-2009 (DE-588)136125484 aut Introduction to stochastic integration K. L. Chung ; R. J. Williams second edition Boston ; Basel ; Berlin Birkhäuser 1990 xv, 276 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Probability and its applications Intégrales stochastiques Intégrales stochastiques ram Martingales (Mathématiques) Martingales (Mathématiques) ram Stochastische integratie gtt Martingales (Mathematics) Stochastic integrals Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Stochastisches Integral (DE-588)4126478-2 s DE-604 Martingal (DE-588)4126466-6 s Williams, Ruth J. 1955- (DE-588)172452910 aut Erscheint auch als Online-Ausgabe 978-1-4612-4480-6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002614534&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Chung, Kai Lai 1917-2009 Williams, Ruth J. 1955- Introduction to stochastic integration Intégrales stochastiques Intégrales stochastiques ram Martingales (Mathématiques) Martingales (Mathématiques) ram Stochastische integratie gtt Martingales (Mathematics) Stochastic integrals Stochastisches Integral (DE-588)4126478-2 gnd Martingal (DE-588)4126466-6 gnd |
| subject_GND | (DE-588)4126478-2 (DE-588)4126466-6 (DE-588)4151278-9 |
| title | Introduction to stochastic integration |
| title_auth | Introduction to stochastic integration |
| title_exact_search | Introduction to stochastic integration |
| title_full | Introduction to stochastic integration K. L. Chung ; R. J. Williams |
| title_fullStr | Introduction to stochastic integration K. L. Chung ; R. J. Williams |
| title_full_unstemmed | Introduction to stochastic integration K. L. Chung ; R. J. Williams |
| title_short | Introduction to stochastic integration |
| title_sort | introduction to stochastic integration |
| topic | Intégrales stochastiques Intégrales stochastiques ram Martingales (Mathématiques) Martingales (Mathématiques) ram Stochastische integratie gtt Martingales (Mathematics) Stochastic integrals Stochastisches Integral (DE-588)4126478-2 gnd Martingal (DE-588)4126466-6 gnd |
| topic_facet | Intégrales stochastiques Martingales (Mathématiques) Stochastische integratie Martingales (Mathematics) Stochastic integrals Stochastisches Integral Martingal Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002614534&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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