This course is offered on the basis of need or interest to graduate/ Ph.D. students, postdocs and other researchers. The recommended prior knowledge is the Math 6040-1 probability course.

Course Description:

This course gives an introduction to Malliavin calculus and its applications to the study of probability laws for diffusion processes. The course will start with Malliavin calculus on a finite Gaussian probability space. Then we will go through the infinite-dimensional differential calculus on the Wiener space. We will introduce the main operators and the associated Sobolev spaces. The second part of this course will discuss the application of this general theory to the analysis of regularity of probability laws of random vectors on the Wiener space. We will study the particular case of diffusion processes, which will take us to a probabilistic proof of Hormander's theorem.

References:

This course will mainly follow the first Chapters of the following books:

The Malliavin calulus and related topics, David Nualart, Springer-Verlag, 1995

Malliavin calculus with applications to stochastic partial differential equations, Marta Sanz-Solé, EPFL Press, 2005