Taking readers with a basic knowledge of probability and real analysis to the frontiers of a
very active research discipline this textbook provides all the necessary background from
functional analysis and the theory of PDEs. It covers the main types of equations (elliptic
hyperbolic and parabolic) and discusses different types of random forcing. The objective is to
give the reader the necessary tools to understand the proofs of existing theorems about SPDEs
(from other sources) and perhaps even to formulate and prove a few new ones. Most of the
material could be covered in about 40 hours of lectures as long as not too much time is spent
on the general discussion of stochastic analysis in infinite dimensions. As the subject of
SPDEs is currently making the transition from the research level to that of a graduate or even
undergraduate course the book attempts to present enough exercise material to fill potential
exams and homework assignments. Exercises appear throughout and are usually directly connected
to the material discussed at a particular place in the text. The questions usually ask to
verify something so that the reader already knows the answer and if pressed for time can
move on. Accordingly no solutions are provided but there are often hints on how to proceed.
The book will be of interest to everybody working in the area of stochastic analysis from
beginning graduate students to experts in the field.
