A01=Yaozhong Hu
Abstract Wiener Space
Author_Yaozhong Hu
Category=PBT
Chaos Expansion
Convergence in Density
Correlation Inequality
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Exponential Integrability
Fock Space
Gaussian Measure
Gaussian Space
HAfA?rmander Theorem
Hermite Polynomials
Hormander Theorem
Hypercontractive Inequality
Hörmander Theorem
Interpolation Inequality
Littlewood-Paley-Stein-Meyer Theory
LittlewoodAcAEURA"PaleyAcAEURA"SteinAcAEURA"Meyer Theory
Littlewood–Paley–Stein–Meyer Theory
Local Time
Logarithmic Inequality
Meyer's Inequality
Multiple Stratonovich Integral
Multiple Wiener-Ita Integral
Multiple WienerAcAEURA"ItAfAc Integral
Multiple Wiener–Itâ Integral
Multiplier Inequality
Non-Explosion
Nonlinear Wiener Functional
Numerical Schemes
PoincarAfA(C) Inequality
Poincare Inequality
Poincaré Inequality
Polarization
Rate of Convergence in Density
Self-Intersection Local Time
Sobolev Space Over Gaussian Space
Stochastic Differential Equation
Strong Rate of Convergence
Weak Rate of Convergence
Wong-Zakai Approximation
Product details
- ISBN 9789813142176
- Publication Date: 18 Oct 2016
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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"Written by a well-known expert in fractional stochastic calculus, this book offers a comprehensive overview of Gaussian analysis, with particular emphasis on nonlinear Gaussian functionals. In addition, it covers some topics that are not frequently encountered in other treatments, such as Littlewood-Paley-Stein, etc. This coverage makes the book a valuable addition to the literature. Many results presented in this book were hitherto available only in the research literature in the form of research papers by the author and his co-authors."Mathematical Reviews ClippingsAnalysis 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.
