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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.

Stochastic differential equations. --- Equations différentielles stochastiques --- Electronic books. -- local. --- Stochastic analysis. --- Stochastic differential equations --- Mathematical Statistics --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- 519.63 --- 681.3*G18 --- Numerical methods for solution of partial differential equations --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.63 Numerical methods for solution of partial differential equations --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Analysis, Stochastic --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- Probabilities. --- Analysis. --- Partial Differential Equations. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Partial differential equations --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- Differential equations --- Fokker-Planck equation --- 681.3 *G18 --- Stochastic processes --- Global analysis (Mathematics). --- Differential equations, partial. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic