An Introduction to Stochastic PDEs

Understand

These notes are based on a series of lectures given first at the University of Warwick in spring 2008 and then at the Courant Institute, Imperial College London, and EPFL.

• It is an attempt to give a reasonably self-contained presentation of the basic theory of stochastic partial differential equations, taking for granted basic measure theory, functional analysis and probability theory, but nothing else.
• The approach taken in these notes is to focus on semilinear parabolic problems driven by additive noise.
• These can be treated as stochastic evolution equations in some infinite-dimensional Banach or Hilbert space that usually have nice regularising properties and they already form a very rich class of problems with many interesting properties.