Introduction to Malliavin calculus
By: Nualart, David
Contributor(s): Nualart, Eulalia
Material type: 
TextSeries: Institute of Mathematical Statistics TextbooksPublisher: New York Cambridge University Press 2018Description: xii, 236 p. Includes bibliographical references and indexISBN: 9781107611986Subject(s): Malliavin calculus | Stochastic analysis | Derivatives - Mathematics | Calculus - variations DDC classification: 519.23 Summary: Description Contents Resources Courses About the Authors
This textbook offers a compact introductory course on Malliavin calculus, an active and powerful area of research. It covers recent applications, including density formulas, regularity of probability laws, central and non-central limit theorems for Gaussian functionals, convergence of densities and non-central limit theorems for the local time of Brownian motion. The book also includes a self-contained presentation of Brownian motion and stochastic calculus, as well as Lévy processes and stochastic calculus for jump processes. Accessible to non-experts, the book can be used by graduate students and researchers to develop their mastery of the core techniques necessary for further study.
Features an up-to-date treatment of the theory, including recent applications
Includes basic preliminary material, making the material accessible to non-experts
Presents a wide overview from different perspectives, providing strong preparation for further study
https://www.cambridge.org/gb/academic/subjects/statistics-probability/probability-theory-and-stochastic-processes/introduction-malliavin-calculus?format=PB
| Item type | Current location | Item location | Collection | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
| Books | Vikram Sarabhai Library General Stacks | Slot 1404 (0 Floor, East Wing) | Non-fiction | 519.23 N8I6 (Browse shelf) | Checked out | 01/07/2021 | 199998 |
Table of Contents
Preface
1. Brownian motion
2. Stochastic calculus
3. Derivative and divergence operators
4. Wiener chaos
5. Ornstein-Uhlenbeck semigroup
6. Stochastic integral representations
7. Study of densities
8. Normal approximations
9. Jump processes
10. Malliavin calculus for jump processes I
11. Malliavin calculus for jump processes II
Appendix A. Basics of stochastic processes
References
Index.
Description Contents Resources Courses About the Authors
This textbook offers a compact introductory course on Malliavin calculus, an active and powerful area of research. It covers recent applications, including density formulas, regularity of probability laws, central and non-central limit theorems for Gaussian functionals, convergence of densities and non-central limit theorems for the local time of Brownian motion. The book also includes a self-contained presentation of Brownian motion and stochastic calculus, as well as Lévy processes and stochastic calculus for jump processes. Accessible to non-experts, the book can be used by graduate students and researchers to develop their mastery of the core techniques necessary for further study.
Features an up-to-date treatment of the theory, including recent applications
Includes basic preliminary material, making the material accessible to non-experts
Presents a wide overview from different perspectives, providing strong preparation for further study
https://www.cambridge.org/gb/academic/subjects/statistics-probability/probability-theory-and-stochastic-processes/introduction-malliavin-calculus?format=PB
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