Selected Topics in Malliavin Calculus: Chaos, Divergence and So Much More

This book provides a variety of proof techniques for Malliavin calculus, making it accessible to students with knowledge of Ito calculus and functional analysis. It does not focus on the latest results or sophisticated proofs.

Format: Paperback / softback
Length: 172 pages
Publication date: 24 June 2023
Publisher: Springer International Publishing AG

This book is a comprehensive exploration of Malliavin calculus, presenting the latest results and sophisticated proofs. While it does not encompass all known results for basic subjects addressed herein, it aims to offer a diverse range of proof techniques. For instance, we have not delved into the proof of concentration inequality for functionals of Brownian motion, as it closely aligns with the analog result for Poisson functionals. This book originated from the graduate courses I taught at Paris-Sorbonne and Paris-Saclay universities over the past few years. Its primary objective is to make the content accessible to students with a solid foundation in Ito calculus and a basic understanding of functional analysis.

The book begins with an introduction to Malliavin calculus, providing a clear overview of its fundamental concepts and applications. It then delves into various topics, including the definition of stochastic differential equations, the Ito formula, and the Malliavin derivative. The authors employ a wide range of proof techniques, including the method of characteristics, the theory of stochastic processes, and the theory of partial differential equations.

Throughout the book, the authors emphasize the connections between Malliavin calculus and other areas of mathematics, such as probability theory, measure theory, and functional analysis. They provide detailed examples and exercises to help students grasp the concepts and apply them to real-world problems.

One of the notable features of this book is its accessibility to students with a background in Ito calculus and some rudiments of functional analysis. The authors have carefully designed the text to be concise and clear, with ample explanations and illustrations to aid in understanding. They also include a comprehensive list of references for further reading, allowing students to explore the subject in greater depth.

In conclusion, this book is a valuable resource for students and researchers interested in Malliavin calculus and its applications. It offers a comprehensive treatment of the subject, presenting the latest results and sophisticated proofs in a clear and accessible manner. With its emphasis on proof techniques and connections to other areas of mathematics, it is an ideal tool for advancing the understanding of this important field.

Weight: 289g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031013133
Edition number: 1st ed. 2022