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.
Transformation of Measure on Wiener Space
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Book Description
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From the Back Cover
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.
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All you wnated to know but did not dare to ask,
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This review is from: Transformation of Measure on Wiener Space (Springer Monographs in Mathematics) (Hardcover)
This book contains everything one needs about the transformations of the Wiener measure under the perturbation of identity-type mappings. It is particularly useful to graduate students in probability, analysis and theoretical physics. It is a pity that there is so few ad about it.
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Inside This Book
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First Sentence:
In this book we study the properties of the image of Wiener measure under several (point) transformations of the flat Wiener space. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
cylindrical functionals, monotone shifts, theoretic degree, indirect shifts, dense vector subspace, cylindrical functions, uniform integrability, sigma algebra, filtered probability space, complete orthonormal basis, degree theorem, continuous martingale, measure induced, local martingale, topological degree, absolute continuity, measurable mapping, degree theory, density argument Key Phrases - Capitalized Phrases (CAPs): (learn more)
H-convex Wiener, H-valued Wiener, Transformations of Measure Induced, Integrability Conditions, Introduction Let, Two Measures Associated New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this book we study the properties of the image of Wiener measure under several (point) transformations of the flat Wiener space. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
cylindrical functionals, monotone shifts, theoretic degree, indirect shifts, dense vector subspace, cylindrical functions, uniform integrability, sigma algebra, filtered probability space, complete orthonormal basis, degree theorem, continuous martingale, measure induced, local martingale, topological degree, absolute continuity, measurable mapping, degree theory, density argument Key Phrases - Capitalized Phrases (CAPs): (learn more)
H-convex Wiener, H-valued Wiener, Transformations of Measure Induced, Integrability Conditions, Introduction Let, Two Measures Associated New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 19
books:
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30
books
cite this book:
See all 30 books citing this book
- Stochastic Analysis (Grundelhren Der Mathematischen Wissenschaften) by Paul Malliavin in Back Matter (1), and Back Matter (2)
- Dirichlet Forms and Symmetric Markov Processes (De Gruyter Studies in Mathematics) by Masatoshi Fukushima in Back Matter
- Probabilities and Potential (Mathematics Studies) by Claude Dellacherie in Back Matter
- Stochastic Integration (Probability and Mathematical Statistics) by Michel Metivier in Back Matter
- Calculus of Variations (Cambridge Studies in Advanced Mathematics) by Jürgen Jost in Back Matter
See all 19 books this book cites
- Valued Fields (Springer Monographs in Mathematics) by Antonio J. Engler in Back Matter
- Lie Algebras and Algebraic Groups (Springer Monographs in Mathematics) by Patrice Tauvel in Back Matter
- Elementary and Analytic Theory of Algebraic Numbers (Springer Monographs in Mathematics) by Wladyslaw Narkiewicz in Back Matter
- Serre's Problem on Projective Modules by T.Y. Lam in Back Matter
- Positive Polynomials: From Hilbert's 17th Problem to Real Algebra (Springer Monographs in Mathematics) by Alexander Prestel in Back Matter
See all 30 books citing this book
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