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Introduction to Malliavin Calculus

Book description

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.

Reviews

'This book is a delightful and self-contained introduction to stochastic and Malliavin calculus that will guide the graduate students in probability theory from the basics of the theory to the borders of contemporary research. It is a must read written by two globally recognized experts!'

Fabrice Baudoin - University of Connecticut

'Malliavin calculus has seen a great revival of interest in recent years, after the discovery about ten years ago that Stein's method for probabilistic approximation and Malliavin calculus fit together admirably well. Such an interaction has led to some remarkable limit theorems for Gaussian, Poisson and Rademacher functionals. This monograph, written by two internationally renowned specialists of the field, provides a concise, self-contained and very pleasant exposition of different aspects of this rich and recent line of research. For sure, it is destined to quickly become a must-have reference book!'

Ivan Nourdin - University of Luxembourg

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