TITLE: Roadmap to SPDEs
QUESTION [19 upvotes]: I'm trying to learn about the Kushner-Stratonovich-Pardoux equations in filtering theory.
I'm familiar with Itô calculus at the level of Øksendal's book (but struggle with much of Karatzas and Shreve, for example).
My PDE theory is pretty weak. I know about the Fokker-Planck equations, and that's about it. My guess is that before I begin reading, I'll need to learn a significant amount of classical PDE theory. I would appreciate any recommendations for PDE textbooks that emphasize material that will be useful in the study of SPDEs. If someone could recommend a gentle introduction to SPDEs to go with it, I would be very grateful.
Many thanks.

REPLY [5 votes]: Rama Cont compiled a rather comprehensive resource page about SPDEs, but some of the links are broken, still this gives you an overview of what books/papers you wanna read in order to know certain aspects of SPDEs.
http://www.cmap.polytechnique.fr/~rama/spde/articles.htm
And don't worry about PDE theory too much, any graduate level PDE textbook, for example L. Evans or Gilbarg and Trudinger, has a too long technicalities introduction, read certain chapters when needed.