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Field name	Details
Dewey Class	515.42
Title	Transformation of Measure on Wiener Space ([EBook] /) / by Ali Süleyman Üstünel, Moshe Zakai.
Author	Üstünel, Ali Süleyman
Added Personal Name	Zakai, Moshe author.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 2000.
Physical Details	XIII, 298 p. : online resource.
Series	Springer monographs in mathematics 1439-7382
ISBN	9783662132258
Summary Note	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. The recent results presented in the book include a dimension-free form of the Girsanov theorem, the transformations of measure induced by anticipative non-invertible shift transformations, the transformation of measure induced by flows, the extension of the notions of Sard lemma and degree theory to Wiener space, generalized distribution valued Radon-Nikodym theorems and measure preserving transformations. Basic probability theory and the Ito calculus are assumed known; the necessary results from the Malliavin calculus are presented in the appendix. Aimed at graduate students and researchers, it can be used as a text for a course or a seminar.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-13225-8
Links to Related Works	Subject References: Functional Analysis . Mathematics . Measure and Integration . Measure theory . Probabilities . Probability theory and stochastic processes . Authors: Üstünel, Ali Süleyman . Zakai, Moshe . Corporate Authors: SpringerLink (Online service) . Series: Springer monographs in mathematics . Classification: 515.42 .

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Transformation of Measure on Wiener Space

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