The Malliavin Calculus And Related Topics

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The Malliavin Calculus And Related Topics

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Author : David Nualart
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-27

The Malliavin Calculus And Related Topics written by David Nualart and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-27 with Mathematics categories.

The Malliavin calculus is an infinite-dimensional differential calculus on a Gaussian space, developed to provide a probabilistic proof to Hörmander's sum of squares theorem but has found a range of applications in stochastic analysis. This book presents the features of Malliavin calculus and discusses its main applications. This second edition includes recent applications in finance and a chapter devoted to the stochastic calculus with respect to the fractional Brownian motion.

The Malliavin Calculus And Related Topics

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Author : David Nualart
language : en
Publisher:
Release Date : 2014-09-01

The Malliavin Calculus And Related Topics written by David Nualart and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.

The Malliavin Calculus And Related Topics

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Author : David Nualart
language : en
Publisher: Springer
Release Date : 2009-09-02

The Malliavin Calculus And Related Topics written by David Nualart and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-02 with Mathematics categories.

The Malliavin calculus is an infinite-dimensional differential calculus on a Gaussian space, developed to provide a probabilistic proof to Hörmander's sum of squares theorem but has found a range of applications in stochastic analysis. This book presents the features of Malliavin calculus and discusses its main applications. This second edition includes recent applications in finance and a chapter devoted to the stochastic calculus with respect to the fractional Brownian motion.

Backward Stochastic Differential Equations

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Author : N El Karoui
language : en
Publisher: CRC Press
Release Date : 1997-01-17

Backward Stochastic Differential Equations written by N El Karoui and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-17 with Mathematics categories.

This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.

Malliavin Calculus And Its Applications

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Author : David Nualart
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Malliavin Calculus And Its Applications written by David Nualart and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

The Malliavin calculus was developed to provide a probabilistic proof of Hormander's hypoellipticity theorem. The theory has expanded to encompass other significant applications. The main application of the Malliavin calculus is to establish the regularity of the probability distribution of functionals of an underlying Gaussian process. In this way, one can prove the existence and smoothness of the density for solutions of various stochastic differential equations. More recently, applications of the Malliavin calculus in areas such as stochastic calculus for fractional Brownian motion, central limit theorems for multiple stochastic integrals, and mathematical finance have emerged. The first part of the book covers the basic results of the Malliavin calculus. The middle part establishes the existence and smoothness results that then lead to the proof of Hormander's hypoellipticity theorem. The last part discusses the recent developments for Brownian motion, central limit theorems, and mathematical finance.

Introduction To Malliavin Calculus

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Author : David Nualart
language : en
Publisher: Cambridge University Press
Release Date : 2018-09-27

Introduction To Malliavin Calculus written by David Nualart and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-27 with Business & Economics categories.

A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.

Differentiable Measures And The Malliavin Calculus

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Author : Vladimir Igorevich Bogachev
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-07-21

Differentiable Measures And The Malliavin Calculus written by Vladimir Igorevich Bogachev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-21 with Mathematics categories.

This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus--a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures. The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.

Stochastic Analysis

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Author : Paul Malliavin
language : en
Publisher: Springer
Release Date : 2015-06-12

Stochastic Analysis written by Paul Malliavin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-12 with Mathematics categories.

This book accounts in 5 independent parts, recent main developments of Stochastic Analysis: Gross-Stroock Sobolev space over a Gaussian probability space; quasi-sure analysis; anticipate stochastic integrals as divergence operators; principle of transfer from ordinary differential equations to stochastic differential equations; Malliavin calculus and elliptic estimates; stochastic Analysis in infinite dimension.

Stochastic Analysis And Related Topics Ii

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Author : Hayri Korezlioglu
language : en
Publisher: Springer
Release Date : 2006-11-14

Stochastic Analysis And Related Topics Ii written by Hayri Korezlioglu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

The Second Silivri Workshop functioned as a short summer school and a working conference, producing lecture notes and research papers on recent developments of Stochastic Analysis on Wiener space. The topics of the lectures concern short time asymptotic problems and anticipative stochastic differential equations. Research papers are mostly extensions and applications of the techniques of anticipative stochastic calculus.

The Poisson Dirichlet Distribution And Related Topics

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Author : Shui Feng
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-27

The Poisson Dirichlet Distribution And Related Topics written by Shui Feng and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-27 with Mathematics categories.

Presenting a comprehensive study of the Poisson-Dirichlet distribution, this volume emphasizes recent progress in evolutionary dynamics and asymptotic behaviors. The self-contained text presents methods and techniques that appeal to researchers in a wide variety of subjects.