Malliavin calculus and its applications
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Bibliographic Information
Malliavin calculus and its applications
（Regional conference series in mathematics, no. 110）
Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society with support from the National Science Foundation, c2009
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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"NSF-CBMS Regional Conferences in the Mathematical Sciences on Malliavin Calculus and Its Applications held at Kent State University, Ohio, August 7-12, 2008"--T.p. verso
Includes bibliographical references (p. 81-83) and index
Description and Table of Contents
Description
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.
by "Nielsen BookData"
