An Introduction to Stochastic PDEs

Details An Introduction to Stochastic PDEs An Introduction to Stochastic PDEs

2009-07-23

arxiv.org/abs/0907.4178v1

Mathematics

Probability

Scientific paper

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.

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