Yaozhong Hu's Books

Integral Transformations and Anticipative Calculus for Fractional Brownian Motions

By: Yaozhong Hu

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Integral Transformations and Anticipative Calculus for Fractional Brownian Motions

By: Yaozhong Hu

A paper that studies two types of integral transformation associated with fractional Brownian motion. They are applied to construct approximation schemes for fractional Brownian motion by polygonal approximation of standard Brownian motion. This approximation is the best in the sense that it minimizes the mean square error.

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Page Count

144

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821837044

ISBN 13

9780821837047

Analysis On Gaussian Spaces

By: Yaozhong Hu

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Analysis On Gaussian Spaces

By: Yaozhong Hu

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.

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Page Count

483

Publisher

World Scientific

Published Date

ISBN 10

9813142197

ISBN 13

9789813142190

Stochastic Calculus for Fractional Brownian Motion and Applications

By: Francesca Biagini,Yaozhong Hu,Bernt Øksendal,Tusheng Zhang

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Stochastic Calculus for Fractional Brownian Motion and Applications

By: Francesca Biagini,Yaozhong Hu,Bernt Øksendal,Tusheng Zhang

The purpose of this book is to present a comprehensive account of the different definitions of stochastic integration for fBm, and to give applications of the resulting theory. Particular emphasis is placed on studying the relations between the different approaches. Readers are assumed to be familiar with probability theory and stochastic analysis, although the mathematical techniques used in the book are thoroughly exposed and some of the necessary prerequisites, such as classical white noise theory and fractional calculus, are recalled in the appendices. This book will be a valuable reference for graduate students and researchers in mathematics, biology, meteorology, physics, engineering and finance.

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Page Count

331

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1846287979

ISBN 13

9781846287978

Regularity and Strict Positivity of Densities for the Nonlinear Stochastic Heat Equations

By: Le Chen,Yaozhong Hu,David Nualart

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Regularity and Strict Positivity of Densities for the Nonlinear Stochastic Heat Equations

By: Le Chen,Yaozhong Hu,David Nualart

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Page Count

102

Publisher

American Mathematical Society

Published Date

ISBN 10

1470450003

ISBN 13

9781470450007

Regularity and Strict Positivity of Densities for the Nonlinear Stochastic Heat Equations

By: Le Chen,Yaozhong Hu,David Nualart

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Regularity and Strict Positivity of Densities for the Nonlinear Stochastic Heat Equations

By: Le Chen,Yaozhong Hu,David Nualart

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Page Count

102

Publisher

American Mathematical Society

Published Date

ISBN 10

1470450003

ISBN 13

9781470450007

Stochastic Calculus for Fractional Brownian Motion and Applications

By: Francesca Biagini,Yaozhong Hu,Bernt Øksendal,Tusheng Zhang

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Stochastic Calculus for Fractional Brownian Motion and Applications

By: Francesca Biagini,Yaozhong Hu,Bernt Øksendal,Tusheng Zhang

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Page Count

330

Publisher

Springer

Published Date

ISBN 10

1849969949

ISBN 13

9781849969949

Analysis on Gaussian Spaces

By: Yaozhong Hu

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Analysis on Gaussian Spaces

By: Yaozhong Hu

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.

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Page Count

470

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9813142170

ISBN 13

9789813142176

Book's by Yaozhong Hu

Integral Transformations and Anticipative Calculus for Fractional Brownian Motions

Integral Transformations and Anticipative Calculus for Fractional Brownian Motions

Analysis On Gaussian Spaces

Analysis On Gaussian Spaces

Stochastic Calculus for Fractional Brownian Motion and Applications

Stochastic Calculus for Fractional Brownian Motion and Applications

Regularity and Strict Positivity of Densities for the Nonlinear Stochastic Heat Equations

Regularity and Strict Positivity of Densities for the Nonlinear Stochastic Heat Equations

Regularity and Strict Positivity of Densities for the Nonlinear Stochastic Heat Equations

Regularity and Strict Positivity of Densities for the Nonlinear Stochastic Heat Equations

Stochastic Calculus for Fractional Brownian Motion and Applications

Stochastic Calculus for Fractional Brownian Motion and Applications

Analysis on Gaussian Spaces

Analysis on Gaussian Spaces

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