Introduction to Malliavin Calculus

A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.

David Nualart (Author), Eulalia Nualart (Author)

9781107039124, Cambridge University Press

Hardback, published 27 September 2018

246 pages
23.6 x 15.7 x 1.8 cm, 0.46 kg

'The book is written very clearly and precisely, and will be useful to anyone who wants to study the Malliavin calculus and its applications at the introductory level and then more deeply, as well as those who are ready to apply these results in their research. The book can be used to give lectures for graduate students.' Yuliya S. Mishura, zbMath

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.

Subject Areas: Mathematical & statistical software [UFM], Stochastics [PBWL], Applied mathematics [PBW], Probability & statistics [PBT], Calculus & mathematical analysis [PBK], Business mathematics & systems [KJQ], Finance [KFF]