Transformation of measure on Wiener space:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
2000
|
| Series: | Springer monographs in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 296 S. graph. Darst. |
| ISBN: | 3540664556 |
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MARC
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| 100 | 1 | |a Üstünel, Ali Süleyman |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Transformation of measure on Wiener space |c A. Süleyman Üstünel; Moshe Zakai |
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| 650 | 4 | |a Malliavin calculus | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction 1
1. Some Background Material and Preliminary Results 5
1.1 The Radon Nikodym Theorem 5
1.2 Uniform Integrability 10
1.3 Two Measures Associated with a Point Transformation 13
1.4 Kakutani s Dichotomy Theorem 16
1.5 The Structure of Non negative Continuous Martingales 17
Notes and References 19
2. Transformation of Measure Induced by Adapted Shifts ... 21
2.1 The Girsanov Theorem 21
2.2 Integrability Conditions on At 25
2.3 Transformation of Measure Induced on Co([0,1]) by
Direct Shifts 28
2.4 Transformations of Measure Induced on Co([0,1]) by Indirect
Shifts 30
2.5 The Innovation Theorem 37
2.6 A Dimension free Extension of Results of the Previous Sections 41
2.7 The Representability of Measures by Shifts 47
Notes and References 51
3. Transformation of Measure Induced by General Shifts .... 53
3.1 Introduction 53
3.2 The Change of Variables Formula for a Small Perturbation of
the Identity 56
3.3 ^/ Regularity of Random Variables 71
3.4 Some Preliminaries 80
3.5 The Change of Variables Formula 86
3.6 A Comparison Between the Formulas Associated with Adapted
and Non Adapted Cases 94
Notes and References 97
XII Contents
4. The Sard Inequality 99
4.1 Introduction and Preliminaries 99
4.2 The Measurability of the Forward Image 102
4.3 The Sard Inequality I 103
4.4 The Sard Inequality II 109
4.5 Some Applications to Absolute Continuity 112
Notes and References 113
5. Transformation of Measure Under Anticipative Flows .... 115
5.1 Introduction and Finite Dimensional Flows 115
5.2 Cylindrical Flows 120
5.3 Infinite Dimensional Flows 127
5.4 A Singular Flow on the Classical Wiener Space 140
Notes and References 156
6. Monotone Shifts 157
6.1 Introduction 157
6.2 Monotone Shifts 158
6.3 Absolute Continuity of Monotone Shifts 1 162
6.4 Absolute Continuity of Monotone Shifts II 171
6.5 Shifts of Hammerstein Type 176
Notes and References 180
7. Generalized Radon Nikodym Derivatives 181
7.1 Introduction 181
7.2 The Q Class of Wiener Functional and its Composition with
Shifts 181
7.2.1 The ?A class of Wiener Functionals 181
7.2.2 The Extendibility of Qx Functionals 184
7.3 A Generalized R N Derivative for Q Functionals 185
7.4 The Conditioning of G Functionals with Respect to Certain
Sub sigma fields 189
7.5 Composition of the Rademacher Class of Wiener Functionals
with Shifts 190
7.6 The Composition Rules 195
7.6.1 The Cylindrical Case 195
7.6.2 Extensions of the Composition Rules 197
Notes and References 205
8. Random Rotations 207
8.1 Introduction 207
8.2 Random Rotations 208
8.3 A Partial Converse to Theorem 8.2.1 216
8.4 The Invertibility of Tw = w + R(w)h and that of R 218
8.5 Stochastic Calculus of Rotations 220
Contents XIII
8.5.1 A New Derivation and Calculation of E[6r) B] 223
8.5.2 Case of Deterministic R 225
8.6 Transformations of Measure Induced by Euclidean Motions
of the Wiener Path 226
Notes and References 231
9. The Degree Theorem on Wiener Space 233
9.1 Introduction 233
9.2 Measure Theoretic Degree 234
9.3 Applications to Absolute Continuity 240
9.4 Relations with Leray Schauder Degree 246
Notes and References 254
A. Some Inequalities 255
A.I Gronwall and Young Inequalities 255
A.1.1 Gronwall Inequality 255
A.I.2 Young Inequality 255
A.2 Some Inequalities for det2(/j7 + A) 256
B. An Introduction to Malliavin Calculus 259
B.I Introduction to Abstract Wiener Space 259
B.2 An Introduction to Analysis on Wiener Space 261
B.3 Construction of Sobolev Derivatives 263
B.4 The Divergence 266
B.5 Ornstein Uhlenbeck Operator and Meyer Inequalities 269
B.6 Some Useful Lemmas 272
B.7 Local Versus Global Differentiability of Wiener Functionals .. 279
B.8 Exponential Integrability of Wiener Functionals and Poincare
Inequality 281
Notes and References 288
References 289
Index 295
Notations 297
|
| any_adam_object | 1 |
| author | Üstünel, Ali Süleyman Zakai, Moshe 1926- |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| indexdate | 2024-07-09T18:34:00Z |
| institution | BVB |
| isbn | 3540664556 |
| language | German |
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| physical | XIII, 296 S. graph. Darst. |
| publishDate | 2000 |
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| spelling | Üstünel, Ali Süleyman Verfasser aut Transformation of measure on Wiener space A. Süleyman Üstünel; Moshe Zakai Berlin [u.a.] Springer 2000 XIII, 296 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Analyse stochastique Malliavin, Calcul de Stochastische analyse gtt Transformaties (wiskunde) gtt Malliavin calculus Stochastic analysis Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Maß Mathematik (DE-588)4037856-1 gnd rswk-swf Transformation (DE-588)4451062-7 gnd rswk-swf Wiener-Raum (DE-588)4189871-0 gnd rswk-swf Stochastisches Integral (DE-588)4126478-2 s Wiener-Raum (DE-588)4189871-0 s Maß Mathematik (DE-588)4037856-1 s Transformation (DE-588)4451062-7 s DE-604 Zakai, Moshe 1926- Verfasser (DE-588)121364372 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008710308&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Üstünel, Ali Süleyman Zakai, Moshe 1926- Transformation of measure on Wiener space Analyse stochastique Malliavin, Calcul de Stochastische analyse gtt Transformaties (wiskunde) gtt Malliavin calculus Stochastic analysis Stochastisches Integral (DE-588)4126478-2 gnd Maß Mathematik (DE-588)4037856-1 gnd Transformation (DE-588)4451062-7 gnd Wiener-Raum (DE-588)4189871-0 gnd |
| subject_GND | (DE-588)4126478-2 (DE-588)4037856-1 (DE-588)4451062-7 (DE-588)4189871-0 |
| title | Transformation of measure on Wiener space |
| title_auth | Transformation of measure on Wiener space |
| title_exact_search | Transformation of measure on Wiener space |
| title_full | Transformation of measure on Wiener space A. Süleyman Üstünel; Moshe Zakai |
| title_fullStr | Transformation of measure on Wiener space A. Süleyman Üstünel; Moshe Zakai |
| title_full_unstemmed | Transformation of measure on Wiener space A. Süleyman Üstünel; Moshe Zakai |
| title_short | Transformation of measure on Wiener space |
| title_sort | transformation of measure on wiener space |
| topic | Analyse stochastique Malliavin, Calcul de Stochastische analyse gtt Transformaties (wiskunde) gtt Malliavin calculus Stochastic analysis Stochastisches Integral (DE-588)4126478-2 gnd Maß Mathematik (DE-588)4037856-1 gnd Transformation (DE-588)4451062-7 gnd Wiener-Raum (DE-588)4189871-0 gnd |
| topic_facet | Analyse stochastique Malliavin, Calcul de Stochastische analyse Transformaties (wiskunde) Malliavin calculus Stochastic analysis Stochastisches Integral Maß Mathematik Transformation Wiener-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008710308&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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