Overview

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.

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