The main goal of this course is to give a systematic introduction to the stochastic integration theory in so-called UMD-Banach spaces developed by Jan van Neerven, Mark Veraar and Lutz Weis in the 2000s. This theory is a cornerstone for establishing maximal regularity for large classes of evolution equations, which model space-time evolutions corrupted by noise.
Since the classical probability theory classes concentrate on finite-dimensional problems, usually the state space being simlply the real line, we will first have to extend concepts like Lebesgue-integration, characteristic function, and Gaussian measures to the Banach space case. These notions at hand we will focus on the relevant Banach space theory, needed for the construction of stochastic integrals in Banach spaces. This includes, in particular, the theory of γ-radonifying operators.
- Lehrende(r): Petru Cioica-Licht