Introduction

This textbook offers a compact introductory course on Malliavin calculus, an active and powerful area of research.

It covers recent applications, including density formulas, regularity of probability laws, central and non-central limit theorems for Gaussian functionals, convergence of densities and non-central limit theorems for the local time of Brownian motion.

The book also includes a self-contained presentation of Brownian motion and stochastic calculus, as well as Lévy processes and stochastic calculus for jump processes.

Accessible to non-experts, the book can be used by graduate students and researchers to develop their mastery of the core techniques necessary for further study.