Selected Topics in Malliavin Calculus: Chaos, Divergence and So Much More - Couverture souple

Decreusefond, Laurent

Couverture souple

ISBN 10 : 3031013131 ISBN 13 : 9783031013133

Editeur : Springer, 2023

Synopsis

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.

A propos du livre

À propos de l'auteur

Laurent Decreusefond is a former student of Ecole Normale Supérieure de Paris-Saclay. He received the Agrégation in 1989, his PhD in 1994 and his Habilitation in 2001 in Mathematics. He is now a full professor of Mathematics at the Institut Polytechnique de Paris, one of the most renowned French research and teaching institutions.
His research topics are twofold. The theoretical part is devoted to Malliavin calculus and its applications. He is the author of a highly cited paper about fractional Brownian motion that paved the way to a thousand research articles. Recently, he has been interested in the functional Stein-Malliavin method, which gives the convergence rate in functional limit theorems.
On a more applied part, he proposed new paradigms for stochastic modelling of telecom systems, including stochastic geometry and random topological algebra.
He coauthored several papers that gavea new approach to the coverage analysis of cellular systems. The performance of some of the algorithms so defined may be analysed with mathematical tools coming from the Malliavin calculus, such as concentration inequalities.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2023
• Langue: anglais
• ISBN 10: 3031013131
• ISBN 13: 9783031013133
• Reliure: Broché
• Nombre de pages: 184
• Coordonnées du fabricant: GPSR Kontakt; ProductSafety@springernature.com; ; Slevogtstraße 3-5; Heidelberg; 69126; Allemagne