Selected Topics in Malliavin Calculus : Chaos, Divergence and So Much More (Bocconi & Springer Series) （2022）

Decreusefond, Laurent

Springer International Publishing AG（2023/06発売）

Springer International Publishing AG（2023/06発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 172 p.
• 商品コード 9783031013133

Full Description

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.

Contents

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