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Transformation of Measure on Wiener Space

(Sprache: Englisch)
Autoren: A. S. Üstünel , Moshe Zakai
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This unique book on the subject addresses fundamental problems and will be the standard reference for a long time to come. The authors have different scientific origins and combine these successfully, creating a text aimed at graduate students and...
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This unique book on the subject addresses fundamental problems and will be the standard reference for a long time to come. The authors have different scientific origins and combine these successfully, creating a text aimed at graduate students and...
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Produktdetails
Produktinformationen zu „Transformation of Measure on Wiener Space “
This unique book on the subject addresses fundamental problems and will be the standard reference for a long time to come. The authors have different scientific origins and combine these successfully, creating a text aimed at graduate students and researchers that can be used for courses and seminars.
Klappentext zu „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). It played an important role in the development of non-anticipative stochastic calculus and itself developed under the impulse of the stochastic calculus of variations. Basic probability theory and the Ito calculus are assumed known; the necessary results from the Malliavin calculus are presented in the appendix. Aimed at graduatestudents and researchers, it can be used as a text for a course or a seminar.
Inhaltsverzeichnis zu „Transformation of Measure on Wiener Space “
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.
Bibliographische Angaben

  • Autoren: A. S. Üstünel , Moshe Zakai
  • 2000, 318 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
  • Verlag: Springer, Berlin
  • ISBN-10: 3540664556
  • ISBN-13: 9783540664550
  • Erscheinungsdatum: 29.11.1999

Sprache:
Englisch
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