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Selected Topics in Malliavin Calculus - Laurent Decreusefond

Selected Topics in Malliavin Calculus

Chaos, Divergence and So Much More
Buch | Softcover
XI, 172 Seiten
2023 | 1st ed. 2022
Springer International Publishing (Verlag)
978-3-031-01313-3 (ISBN)
CHF 67,35 inkl. MwSt
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 Ito calculus and some rudiments of functional analysis.

lt;b>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 gave a 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.

- 1. Wiener Space. - 2. Gradient and Divergence. - 3. Wiener Chaos. - 4. Fractional Brownian Motion. - 5. Poisson Space. - 6. The Malliavin-Stein Method.

"For all the notions, precise definitions of the mathematical objects and complete proofs of the results are given; some examples are thoroughly studied. At the end of each chapter, the reader can also find some classical mathematical background. This book should prove useful for students and academic scholars wishing to get acquainted with Malliavin's calculus, and also for more advanced researchers interested by more recent applications." (Jean Picard, zbMATH 1514.60002, 2023)

“For all the notions, precise definitions of the mathematical objects and complete proofs of the results are given; some examples are thoroughly studied. At the end of each chapter, the reader can also find some classical mathematical background. This book should prove useful for students and academic scholars wishing to get acquainted with Malliavin’s calculus, and also for more advanced researchers interested by more recent applications.” (Jean Picard, zbMATH 1514.60002, 2023)

Erscheinungsdatum
Reihe/Serie Bocconi & Springer Series
Zusatzinfo XI, 172 p. 4 illus., 1 illus. in color.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 288 g
Themenwelt Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Schlagworte Brownian motion • Fractional Brownian motion • Malliavin calculus • Malliavin Gradient • Poisson process • Stein's method • Wiener chaos • Wiener space
ISBN-10 3-031-01313-1 / 3031013131
ISBN-13 978-3-031-01313-3 / 9783031013133
Zustand Neuware
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