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Cover: 9783031013102 | Selected Topics in Malliavin Calculus | Laurent Decreusefond | Buch
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Selected Topics in Malliavin Calculus
Chaos, Divergence and So Much More
Buch von Laurent Decreusefond
Sprache: Englisch

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Beschreibung
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 Itö calculus and some rudiments of functional analysis.
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 Itö calculus and some rudiments of functional analysis.
Über 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.
Zusammenfassung

Provides a pedagogical and self-contained introduction to Malliavin calculus

Covers some of the most modern applications of Malliavin calculus like the Malliavin-Stein method

Illustrates the links between Malliavin calculus and functional analysis in measure space

Inhaltsverzeichnis
- 1. Wiener Space. - 2. Gradient and Divergence. - 3. Wiener Chaos. - 4. Fractional Brownian Motion. - 5. Poisson Space. - 6. The Malliavin-Stein Method.
Details
Erscheinungsjahr: 2022
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Bocconi & Springer Series
Inhalt: xi
172 S.
3 s/w Illustr.
1 farbige Illustr.
172 p. 4 illus.
1 illus. in color.
ISBN-13: 9783031013102
ISBN-10: 3031013107
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Decreusefond, Laurent
Auflage: 1st ed. 2022
Hersteller: Springer International Publishing
Springer International Publishing AG
Bocconi & Springer Series
Maße: 241 x 160 x 16 mm
Von/Mit: Laurent Decreusefond
Erscheinungsdatum: 24.06.2022
Gewicht: 0,448 kg
Artikel-ID: 121325578
Über 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.
Zusammenfassung

Provides a pedagogical and self-contained introduction to Malliavin calculus

Covers some of the most modern applications of Malliavin calculus like the Malliavin-Stein method

Illustrates the links between Malliavin calculus and functional analysis in measure space

Inhaltsverzeichnis
- 1. Wiener Space. - 2. Gradient and Divergence. - 3. Wiener Chaos. - 4. Fractional Brownian Motion. - 5. Poisson Space. - 6. The Malliavin-Stein Method.
Details
Erscheinungsjahr: 2022
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Bocconi & Springer Series
Inhalt: xi
172 S.
3 s/w Illustr.
1 farbige Illustr.
172 p. 4 illus.
1 illus. in color.
ISBN-13: 9783031013102
ISBN-10: 3031013107
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Decreusefond, Laurent
Auflage: 1st ed. 2022
Hersteller: Springer International Publishing
Springer International Publishing AG
Bocconi & Springer Series
Maße: 241 x 160 x 16 mm
Von/Mit: Laurent Decreusefond
Erscheinungsdatum: 24.06.2022
Gewicht: 0,448 kg
Artikel-ID: 121325578
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