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The Malliavin calculus is an infinite-dimensional differential calculus on a Gaussian space, developed to provide a probabilistic proof to Hormander's sum of squares theorem but has found a range of a

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.

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.

Highly technical monograph in which the authors, writing on the basis of their own recent research for the benefit of expert readers, describe a general theory of stochastic integration appropriate to

Stroock, Daniel W.: Some applications of stochastic calculus to partial differential equations.- Ikeda, Nobuyuki: Probabilistic methods in the study of asymptotics.- Nualart, David: Analysis on Wiener

This book introduces some advanced topics in probability theories - both pure and applied. It is divided into two parts: the first part deals with the analysis of stochastic dynamical systems, in term

Concentration inequalities, which express the fact that certain complicated random variables are almost constant, have proven of utmost importance in many areas of probability and statistics. This vol

In May 2006, The University of Utah hosted an NSF-funded minicourse on stochastic partial differential equations. The goal of this minicourse was to introduce graduate students and recent Ph.D.s to va

This volume contains twenty refereed papers presented at the 4th Seminar on Stochastic Processes, Random Fields and Applications, which took place in Ascona, Switzerland, from May 2002. The seminar fo