David Nualart

Introduction to Malliavin Calculus (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 27. September 2018
• Englisch
• ISBN-13: 9781108644402
• Artikelnr.: 56569122

Autorenporträt

David Nualart is the Black-Babcock Distinguished Professor in the Department of Mathematics at the University of Kansas. He has published around 300 scientific articles in the field of probability and stochastic processes, and he is the author of the fundamental monograph The Malliavin Calculus and Related Topics (2005). He has served on the editorial board of leading journals in probability, and from 2006 to 2008 was the editor-in-chief of Electronic Communications in Probability. He was elected Fellow of the Institute of Mathematical Statistics in 1997 and he received the Higuchi Award on Basic Sciences in 2015.

Inhaltsangabe

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.