Selected Topics in Malliavin Calculus

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Selected Topics in Malliavin Calculus is written by Laurent Decreusefond and published by Springer Nature. It's available with International Standard Book Number or ISBN identification 3031013115 (ISBN 10) and 9783031013119 (ISBN 13).

This book is not a research monograph about Malliavin calculus with the latest results and the most sophisticated proofs. It does not contain all the results which are known even for the basic subjects which are addressed here. The goal was to give the largest possible variety of proof techniques. For instance, we did not focus on the proof of concentration inequality for functionals of the Brownian motion, as it closely follows the lines of the analog result for Poisson functionals. This book grew from the graduate courses I gave at Paris-Sorbonne and Paris-Saclay universities, during the last few years. It is supposed to be as accessible as possible for students who have knowledge of Itô calculus and some rudiments of functional analysis.