A Concise Course on Stochastic Partial Differential Equations

Name: A Concise Course on Stochastic Partial Differential Equations
Brand: Springer Nature
SKU: 9783540707813
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Springer Nature

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9783540707813

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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.

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