Analysis on Gaussian Spaces

Analysis on Gaussian Spaces

Author: Yaozhong Hu

Publisher: World Scientific

ISBN: 9789813142190

Category: Mathematics

Page: 484

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Analysis of functions on the finite dimensional Euclidean space with respect to the Lebesgue measure is fundamental in mathematics. The extension to infinite dimension is a great challenge due to the lack of Lebesgue measure on infinite dimensional space. Instead the most popular measure used in infinite dimensional space is the Gaussian measure, which has been unified under the terminology of "abstract Wiener space". Out of the large amount of work on this topic, this book presents some fundamental results plus recent progress. We shall present some results on the Gaussian space itself such as the Brunn–Minkowski inequality, Small ball estimates, large tail estimates. The majority part of this book is devoted to the analysis of nonlinear functions on the Gaussian space. Derivative, Sobolev spaces are introduced, while the famous Poincaré inequality, logarithmic inequality, hypercontractive inequality, Meyer's inequality, Littlewood–Paley–Stein–Meyer theory are given in details. This book includes some basic material that cannot be found elsewhere that the author believes should be an integral part of the subject. For example, the book includes some interesting and important inequalities, the Littlewood–Paley–Stein–Meyer theory, and the Hörmander theorem. The book also includes some recent progress achieved by the author and collaborators on density convergence, numerical solutions, local times.
Analysis on Gaussian Spaces
Language: en
Pages: 484
Authors: Yaozhong Hu
Categories: Mathematics
Type: BOOK - Published: 2016-08-30 - Publisher: World Scientific

Analysis of functions on the finite dimensional Euclidean space with respect to the Lebesgue measure is fundamental in mathematics. The extension to infinite dimension is a great challenge due to the lack of Lebesgue measure on infinite dimensional space. Instead the most popular measure used in infinite dimensional space is
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Language: en
Pages: 346
Authors: Peter K. Friz, Martin Hairer
Categories: Mathematics
Type: BOOK - Published: 2020-05-27 - Publisher: Springer Nature

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Language: en
Pages: 336
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Categories: Mathematics
Type: BOOK - Published: 1994-08-22 - Publisher: CRC Press

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Pages: 454
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Type: BOOK - Published: 1995-01-01 - Publisher: Walter de Gruyter

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Regularity and Strict Positivity of Densities for the Nonlinear Stochastic Heat Equations
Language: en
Pages: 102
Authors: Le Chen, Yaozhong Hu, David Nualart
Categories: Mathematics
Type: BOOK - Published: 2021-12-09 - Publisher: American Mathematical Society

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