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＜電子ブック＞
Transformation of Measure on Wiener Space / by A.Süleyman Üstünel, Moshe Zakai
(Springer Monographs in Mathematics. ISSN:21969922)

版	1st ed. 2000.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2000
本文言語	英語
大きさ	XIII, 298 p : online resource
著者標目	*Üstünel, A.Süleyman author Zakai, Moshe author SpringerLink (Online service)
件　名	LCSH:Measure theory LCSH:Functional analysis LCSH:Probabilities FREE:Measure and Integration FREE:Functional Analysis FREE:Probability Theory
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-662-13225-8

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