Transformation of Measure on Wiener Space
This book gives a systematic presentation of the main results on the transformation of measure induced by shift transformations on Wiener space. This topic has its origins in the work of Cameron and Martin (anticipative shifts, 1940's) and that of Girsanov (non-anticipative shifts, 1960's)...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2000, 2000
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| Edition: | 1st ed. 2000 |
| Series: | Springer Monographs in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. Some Background Material and Preliminary Results
- 2. Transformation of Measure Induced by Adapted Shifts
- 3. Transformation of Measure Induced by General Shifts
- 4. The Sard Inequality
- 5. Transformation of Measure Under Anticipative Flows
- 6. Monotone Shifts
- 7. Generalized Radon-Nikodym Derivatives
- 8. Random Rotations
- 9. The Degree Theorem on Wiener Space
- A. Some Inequalities
- A.1 Gronwall and Young Inequalities
- A.1.1 Gronwall Inequality
- A.1.2 Young Inequality
- B. An Introduction to Malliavin Calculus
- B.1 Introduction to Abstract Wiener Space
- B.2 An Introduction to Analysis on Wiener Space
- B.3 Construction of Sobolev Derivatives
- B.4 The Divergence
- B.5 Ornstein-Uhlenbeck Operator and Meyer Inequalities
- B.6 Some Useful Lemmas
- B.7 Local Versus Global Differentiability of Wiener Functionals
- B.8 Exponential Integrability of Wiener Functionals and Poincaré Inequality
- Notes and References
- References
- Notations