Stochastic partial differential equations (SPDEs, for short) are mathematical models for evolutions in space and time that are influenced by noise. Over the past fifty years the sub- ject of SPDEs evolved into one of the most active areas of research in probability theory. It lies at the crossroads of the theory of stochastic processes and partial differential equations and has applications ranging from fluid dynamics to epidemiology to financial modelling.
The main goal of this course is to give a systematic introduction to the theory of SPDEs. On the one hand, we are going to extend probabilistic notions like Gaussian measures, Brownian motions, and stochastic Itô integrals to an infinite-dimensional setting. On the other hand, we are going to deal with some functional analytic notions like Hilbert-Schmidt and trace class operators or semigroups, which occur naturally when talking about SPDEs. Based on these building blocks we will be able to give a rigorous meaning to some relevant classes of SPDEs and establish existence and uniqueness of solutions.
- Lehrende(r): Petru Cioica-Licht
- Lehrende(r): Martin Hutzenthaler