Introduction to Malliavin Calculus

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 Lvy 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.