Probability and Its Applications

The Malliavin Calculus and Related Topics

Authors: Nualart, David

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  • ISBN 978-3-540-28329-4
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About this book

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.

Reviews

From the reviews of the second edition:

"Nualart’s book serves both pedagogic and research needs. On the one hand, it is written to teach the subject. … On the other hand, the applications in the book are sufficiently broad and in depth that the reader who masters them should be prepared for research. … Furthermore, the unified approach and the careful statement of technical results in the development of the applications make the text a handy reference for researchers. … The bibliography is extensive and has been updated." (Daniel Ocone, Mathematical Reviews, Issue 2006 j)


Table of contents (1 chapters)

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-540-28329-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-540-28328-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-3-642-06651-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Malliavin Calculus and Related Topics
Authors
Series Title
Probability and Its Applications
Copyright
2006
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-28329-4
DOI
10.1007/3-540-28329-3
Hardcover ISBN
978-3-540-28328-7
Softcover ISBN
978-3-642-06651-1
Series ISSN
1431-7028
Edition Number
2
Number of Pages
XIV, 382
Topics