An Introduction to Malliavin Calculus

Malliavin calculus provides a powerful framework for analyzing the probabilistic characteristics of stochastic differential equations. This chapter offers a self-contained introduction to its fundamental elements, including the Wiener–Itô chaos expansion, Malliavin derivative, Skorohod integral, Ornstein–Uhlenbeck operator, and Malliavin–Sobolev spaces. Furthermore, we present criteria for the existence and smoothness of densities of Wiener functionals, along with results on the convergence of density approximations.