Electronic ISBN:  9781470415686 
Product Code:  CBMS/110.E 
List Price:  $31.00 
MAA Member Price:  $27.90 
AMS Member Price:  $24.80 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 110; 2009; 85 ppMSC: Primary 60;
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 copublication of the AMS and CBMS.
ReadershipGraduate students and research mathematicians interested in probability, the Malliavin calculus, and stochastic partial differential equations.

Table of Contents

Chapters

Chapter 1. The derivative operator

Chapter 2. The divergence operator

Chapter 3. The OrnsteinUhlenbeck semigroup

Chapter 4. Sobolev spaces and equivalence of norms

Chapter 5. Regularity of probability laws

Chapter 6. Support properties. Density of the maximum

Chapter 7. Application of Malliavin calculus to diffusion processes

Chapter 8. The divergence operator as a stochastic integral

Chapter 9. Central limit theorems and Malliavin calculus

Chapter 10. Applications of Malliavin calculus in finance


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

Chapters

Chapter 1. The derivative operator

Chapter 2. The divergence operator

Chapter 3. The OrnsteinUhlenbeck semigroup

Chapter 4. Sobolev spaces and equivalence of norms

Chapter 5. Regularity of probability laws

Chapter 6. Support properties. Density of the maximum

Chapter 7. Application of Malliavin calculus to diffusion processes

Chapter 8. The divergence operator as a stochastic integral

Chapter 9. Central limit theorems and Malliavin calculus

Chapter 10. Applications of Malliavin calculus in finance