An Introduction to SPDE's

Catalog description

An introduction to the basic theory of Stochastic PDE's. Topics will likely include (time permitting) Gaussian measure theory, stochastic integration, stochastic convolutions, stochastic evolution equations in Hilbert spaces, Ito's formula, local well-posedness for semi-linear SPDE with additive noise, weak Martingale solutions to 3D Navier-Stokes, Markov processes on Polish spaces, the Krylov–Bogolyubov theorem, the Doob-Khasminskii theorem, and Bismut-Elworthy-Li formula for a class of non-degenerate SPDE. The presentation will be largely self contained, but will assume some basic knowledge in measure theory, functional analysis, and probability theory. Some familiarity with SDE and PDE is also very helpful, but not required.