ISBN: 9783540283287

There have been ten years since the publication of the ?rst edition of this book. Since then, new applications and developments of the Malliavin c- culus have appeared. In preparing this … More...

There have been ten years since the publication of the ?rst edition of this book. Since then, new applications and developments of the Malliavin c- culus have appeared. In preparing this second edition we have taken into account some of these new applications, and in this spirit, the book has two additional chapters that deal with the following two topics: Fractional Brownian motion and Mathematical Finance. The presentation of the Malliavin calculus has been slightly modi?ed at some points, where we have taken advantage of the material from the lecturesgiveninSaintFlourin1995(seereference[248]).Themainchanges and additional material are the following: In Chapter 1, the derivative and divergence operators are introduced in the framework of an isonormal Gaussian process associated with a general 2 Hilbert space H. The case where H is an L -space is trated in detail aft- s, p wards (white noise case). The Sobolev spaces D , with s is an arbitrary real number, are introduced following Watanabe''s work. Chapter2includesageneralestimateforthedensityofaone-dimensional random variable, with application to stochastic integrals. Also, the c- position of tempered distributions with nondegenerate random vectors is discussed following Watanabe''s ideas. This provides an alternative proof of the smoothness of densities for nondegenerate random vectors. Some properties of the support of the law are also presented. | The Malliavin Calculus and Related Topics by David Nualart Hardcover | Indigo Chapters Books > Science & Nature > Math & Physics > Mathematics > Probability & Statistics P10117, David Nualart<

ISBN: 9783540283287

There have been ten years since the publication of the ?rst edition of this book. Since then, new applications and developments of the Malliavin c- culus have appeared. In preparing this … More...

There have been ten years since the publication of the ?rst edition of this book. Since then, new applications and developments of the Malliavin c- culus have appeared. In preparing this second edition we have taken into account some of these new applications, and in this spirit, the book has two additional chapters that deal with the following two topics: Fractional Brownian motion and Mathematical Finance. The presentation of the Malliavin calculus has been slightly modi?ed at some points, where we have taken advantage of the material from the lecturesgiveninSaintFlourin1995(seereference[248]).Themainchanges and additional material are the following: In Chapter 1, the derivative and divergence operators are introduced in the framework of an isonormal Gaussian process associated with a general 2 Hilbert space H. The case where H is an L -space is trated in detail aft- s,p wards (white noise case). The Sobolev spaces D , with s is an arbitrary real number, are introduced following Watanabe''s work. Chapter2includesageneralestimateforthedensityofaone-dimensional random variable, with application to stochastic integrals. Also, the c- position of tempered distributions with nondegenerate random vectors is discussed following Watanabe''s ideas. This provides an alternative proof of the smoothness of densities for nondegenerate random vectors. Some properties of the support of the law are also presented. Books > Science & Nature > Math & Physics > Mathematics > Probability & Statistics List_Books, [PU: Springer, Berlin/Heidelberg]<

ISBN: 9783540283287

There have been ten years since the publication of the ?rst edition of this book. Since then, new applications and developments of the Malliavin c- culus have appeared. In preparing this … More...

There have been ten years since the publication of the ?rst edition of this book. Since then, new applications and developments of the Malliavin c- culus have appeared. In preparing this second edition we have taken into account some of these new applications, and in this spirit, the book has two additional chapters that deal with the following two topics: Fractional Brownian motion and Mathematical Finance. The presentation of the Malliavin calculus has been slightly modi?ed at some points, where we have taken advantage of the material from the lecturesgiveninSaintFlourin1995(seereference[248]).Themainchanges and additional material are the following: In Chapter 1, the derivative and divergence operators are introduced in the framework of an isonormal Gaussian process associated with a general 2 Hilbert space H. The case where H is an L -space is trated in detail aft- s,p wards (white noise case). The Sobolev spaces D , with s is an arbitrary real number, are introduced following Watanabe’s work. Chapter2includesageneralestimateforthedensityofaone-dimensional random variable, with application to stochastic integrals. Also, the c- position of tempered distributions with nondegenerate random vectors is discussed following Watanabe’s ideas. This provides an alternative proof of the smoothness of densities for nondegenerate random vectors. Some properties of the support of the law are also presented., Springer<

2006, ISBN: 9783540283287

[ED: Hardcover], [PU: Springer, Berlin], The Malliavin calculus (or stochastic calculus of variations) is an infinite-dimensional differential calculus on a Gaussian space. Originally, it… More...

[ED: Hardcover], [PU: Springer, Berlin], The Malliavin calculus (or stochastic calculus of variations) is an infinite-dimensional differential calculus on a Gaussian space. Originally, it was developed to provide a probabilistic proof to Hörmander's "sum of squares" theorem, but it has found a wide range of applications in stochastic analysis. This monograph presents the main features of the Malliavin calculus and discusses in detail its main applications. The author begins by developing the analysis on the Wiener space, and then uses this to establish the regularity of probability laws and to prove Hörmander's theorem. The regularity of the law of stochastic partial differential equations driven by a space-time white noise is also studied. The subsequent chapters develop the connection of the Malliavin with the anticipating stochastic calculus, studying anticipating stochastic differential equations and the Markov of solutions to stochastic differential equations with boundary conditions. The second edition of this monograph includes recent applications of the Malliavin calculus in finance and a chapter devoted to the stochastic calculus with respect to the fractional Brownian motion. 2nd ed. 2006. xiv, 382 S. XIV, 382 p. 243 x 177 mm Versandfertig in 3-5 Tagen, DE, [SC: 0.00], Neuware, gewerbliches Angebot, Offene Rechnung (Vorkasse vorbehalten)<

2006, ISBN: 9783540283287

The Malliavin Calculus and Related Topics ab 149.99 € als gebundene Ausgabe: 2nd ed. 2006. Aus dem Bereich: Bücher, Wissenschaft, Mathematik, Medien > Bücher nein Buch (gebunden) Hardcove… More...

The Malliavin Calculus and Related Topics ab 149.99 € als gebundene Ausgabe: 2nd ed. 2006. Aus dem Bereich: Bücher, Wissenschaft, Mathematik, Medien > Bücher nein Buch (gebunden) Hardcover;Naturwissenschaften, Medizin, Informatik, Technik;Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik, Springer Berlin Heidelberg<