This seminar is currently run fully online.

Topic: Introduction to SPDEs in Hilbert spaces

This series will provide an introduction to stochastic partial differential equations (SPDEs). We will take the ‘classical’ Da Prato-Zabczyk approach, i.e. we interpret the SPDE as a stochastic differential equation (SDE) in a Hilbert space.  More specifically, we will discuss the following topics:

• Gaussian measures in Hilbert spaces and the construction of a Brownian motion in a Hilbert space
• Stochastic calculus and martingales in Hilbert spaces: Itô’s isometry, Burkholder-Davis-Gundy inequalities
• Semigroup theory: analytic semigroups
• Well-posedness of SDEs in a Hilbert space
• Examples of SPDEs that fit in the treated framework

If time permits, we can briefly dwell upon SPDEs with monotone coefficients, numerical methods for SPDEs, or the technicalities that arise when extending the above-mentioned theory to the Banach space setting.

The course consists of 10–12 one-hour meetings. Participants may be asked to present some of the material.