Introduction to Malliavin calculus
著者
書誌事項
Introduction to Malliavin calculus
（Institute of Mathematical Statistics textbooks, 9）
Cambridge University Press, 2018
- : hardback
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注記
Includes bibliographical references (p. 228-233) and index
内容説明・目次
内容説明
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 Levy 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.
目次
- 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.
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