Yaozhong Hu: Introduction to Malliavin Caluculus

Abstract:

This course offers an introduction to Malliavin calculus (stochastic calculus of variations). We develop tools on Gaussian spaces to study smoothness of distributions and densities of random variables.

Topics:

• Gaussian measures in finite-dimensional spaces
• Hypercontractivity and logarithmic Sobolev inequality
• Canonical Wiener measure and Brownian motion
• Gross–Sobolev–Malliavin derivatives
• Meyer’s inequality; integration by parts
• Existence and smoothness of densities
• Malliavin–Stein method; convergence to Gaussian and other densities

More information:

sites.google.com/view/introduction-to-malliavin-calc/home

Schedule:

Lectures will be given online. Times to be announced in September.