An introduction to Malliavin calculus

Abstract

Malliavin calculus has been introduced by Malliavin in 70s in order to provide a probabilistic proof of Hormander’s Theorem, but it turned out to have many applications in many different fields, such as finance and stochastic differential equations. In this talk I present the mail tools which allow to define Sobolev spaces of random variables, starting from the 1-dimensional case to get up to the infinite dimensional setting.