A concise course on stochastic partial differential equations

Claudia Prévôt, Michael Röckner (auth.)3540707808, 9783540707806

These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations.
To keep the technicalities minimal we confine ourselves to the case where the noise term is given by a stochastic integral w.r.t. a cylindrical Wiener process.But all results can be easily generalized to SPDE with more general noises such as, for instance, stochastic integral w.r.t. a continuous local martingale.

There are basically three approaches to analyze SPDE: the “martingale measure approach”, the “mild solution approach” and the “variational approach”. The purpose of these notes is to give a concise and as self-contained as possible an introduction to the “variational approach”. A large part of necessary background material, such as definitions and results from the theory of Hilbert spaces, are included in appendices.

Table of contents :
Front Matter….Pages V-VI
Motivation, Aims and Examples….Pages 1-4
Stochastic Integral in Hilbert Spaces….Pages 5-42
Stochastic Differential Equations in Finite Dimensions….Pages 43-54
A Class of Stochastic Differential Equations….Pages 55-103
Back Matter….Pages 105-148