**CBMS Regional Conference Series in Mathematics**

Volume: 110;
2009;
85 pp;
Softcover

MSC: Primary 60;

Print ISBN: 978-0-8218-4779-4

Product Code: CBMS/110

List Price: $31.00

Individual Price: $24.80

**Electronic ISBN: 978-1-4704-1568-6
Product Code: CBMS/110.E**

List Price: $31.00

Individual Member Price: $24.80

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#### Supplemental Materials

# Malliavin Calculus and Its Applications

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*David Nualart*

A co-publication of the AMS and CBMS

The Malliavin calculus was developed to provide a probabilistic proof of
Hörmander'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 Hörmander's hypoellipticity
theorem. The last part discusses the recent developments for Brownian
motion, central limit theorems, and mathematical finance.

A co-publication of the AMS and CBMS.

#### Readership

Graduate students and research mathematicians interested in probability, the Malliavin calculus, and stochastic partial differential equations.

#### Table of Contents

# Table of Contents

## Malliavin Calculus and Its Applications

- Cover Cover11 free
- Half title page i3 free
- Title page iii5 free
- Contents v7 free
- Preface vii9 free
- The derivative operator 111 free
- The divergence operator 1323
- The Ornstein-Uhlenbeck semigroup 1929
- Sobolev spaces and equivalence of norms 2737
- Regularity of probability laws 3343
- Support properties. Density of the maximum 3949
- Application of Malliavin calculus to diffusion processes 4555
- The divergence operator as a stochastic integral 5565
- Central limit theorems and Malliavin calculus 6777
- Applications of Malliavin calculus in finance 7585
- Bibliography 8191
- Index 8595 free
- Back Cover Back Cover199