Introduction to Malliavin Calculus: 9 (Institute of Mathematical Statistics Textbooks, Series Number 9)
Cambridge University Press, 9/27/2018
EAN 9781107039124, ISBN10: 1107039126
Hardcover, 246 pages, 23.6 x 15.7 x 1.8 cm
Language: English
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.
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.