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Selected Topics in Malliavin Calculus: Chaos, Divergence and So Much More (Bocconi & Springer Series, Band 10) - Softcover

Decreusefond, Laurent

 
9783031013133: Selected Topics in Malliavin Calculus: Chaos, Divergence and So Much More (Bocconi & Springer Series, Band 10)
Softcover
ISBN 10: 3031013131 ISBN 13: 9783031013133
Verlag: Springer, 2023

Inhaltsangabe

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.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Über die Autorin bzw. den Autor

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.

Von der hinteren Coverseite

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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Springer
Erscheinungsdatum
2023
Sprache
Englisch
ISBN 10 
3031013131
ISBN 13 
9783031013133
Einband
Taschenbuch
Auflage
1
Anzahl der Seiten
184
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