An Introduction to Stochastic PDEs
(2009)cite arxiv:0907.4178.Abstract
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 in spring 2009. 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. Furthermore, this class of problems
has the advantage of allowing to completely pass under silence many subtle
problems arising from stochastic integration in infinite-dimensional spaces.
