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Malliavin Calculus and Its Applications
     

Malliavin Calculus and Its Applications

by David Nualart
 

ISBN-10: 0821847791

ISBN-13: 9780821847794

Pub. Date: 05/13/2009

Publisher: American Mathematical Society

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

Overview

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.

Product Details

ISBN-13:
9780821847794
Publisher:
American Mathematical Society
Publication date:
05/13/2009
Series:
CBMS Regional Conference Series in Mathematics Ser. , #110
Edition description:
New Edition
Pages:
85
Product dimensions:
6.70(w) x 9.80(h) x 0.30(d)

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