Selected Topics in Malliavin Calculus
Selected Topics in Malliavin Calculus
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Summary
This book is not a research monograph about Malliavin calculus with the latest results and the most sophisticated proofs. 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.
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Selected Topics in Malliavin Calculus by Laurent Decreusefond
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.
“For all the notions, precise definitions of the mathematical objects and complete proofs of the results are given; some examples are thoroughly studiedAt 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)
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.
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.
| SKU | Unavailable |
| ISBN 13 | 9783031013133 |
| ISBN 10 | 3031013131 |
| Title | Selected Topics in Malliavin Calculus |
| Author | Laurent Decreusefond |
| Series | Bocconi And Springer Series |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer International Publishing AG |
| Year published | 2023-06-25 |
| Number of pages | 172 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |