Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
Please make all selections above before adding to cart
Copy To Clipboard
Successfully Copied!
Differentiable Measures and the Malliavin Calculus

Vladimir I. Bogachev Moscow State University, Moscow, Russia
Available Formats:
Hardcover ISBN: 978-0-8218-4993-4
Product Code: SURV/164
List Price: $120.00 MAA Member Price:$108.00
AMS Member Price: $96.00 Electronic ISBN: 978-1-4704-1391-0 Product Code: SURV/164.E List Price:$113.00
MAA Member Price: $101.70 AMS Member Price:$90.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $180.00 MAA Member Price:$162.00
AMS Member Price: $144.00 Click above image for expanded view Differentiable Measures and the Malliavin Calculus Vladimir I. Bogachev Moscow State University, Moscow, Russia Available Formats:  Hardcover ISBN: 978-0-8218-4993-4 Product Code: SURV/164  List Price:$120.00 MAA Member Price: $108.00 AMS Member Price:$96.00
 Electronic ISBN: 978-1-4704-1391-0 Product Code: SURV/164.E
 List Price: $113.00 MAA Member Price:$101.70 AMS Member Price: $90.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$180.00 MAA Member Price: $162.00 AMS Member Price:$144.00
• Book Details

Mathematical Surveys and Monographs
Volume: 1642010; 488 pp
MSC: Primary 28; 46; 58; 60;

This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus—a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures.

The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.

Graduate students and research mathematicians interested in measure theory and random processes.

• Chapters
• 1. Background material
• 2. Sobolev spaces on $\mathbb {R}^n$
• 3. Differentiable measures on linear spaces
• 4. Some classes of differentiable measures
• 5. Subspaces of differentiability of measures
• 6. Integration by parts and logarithmic derivatives
• 7. Logarithmic gradients
• 8. Sobolev classes on infinite dimensional spaces
• 9. The Malliavin calculus
• 10. Infinite dimensional transformations
• 11. Measures on manifolds
• 12. Applications

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1642010; 488 pp
MSC: Primary 28; 46; 58; 60;

This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus—a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures.

The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.

Graduate students and research mathematicians interested in measure theory and random processes.

• Chapters
• 1. Background material
• 2. Sobolev spaces on $\mathbb {R}^n$
• 3. Differentiable measures on linear spaces
• 4. Some classes of differentiable measures
• 5. Subspaces of differentiability of measures
• 6. Integration by parts and logarithmic derivatives
• 7. Logarithmic gradients
• 8. Sobolev classes on infinite dimensional spaces
• 9. The Malliavin calculus
• 10. Infinite dimensional transformations
• 11. Measures on manifolds
• 12. Applications
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.