Concise Course on Stochastic Partial Differential Equations
«A Concise Course on Stochastic Partial Differential Equations (Lecture Notes in Mathematics)»
Claudia Prévôt / Michael Röckner | Springer | 3540707808 | 1 edition (July 2007) | 148 pages | PDF | 1.5 MB
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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Stochastic Partial Differential Equations Partial Differential Equations Martingale Measure Partial Differential Equations Lecture Notes Stochastic Integral Concise Course Variational Approach Wiener Process Mild Solution Hilbert Spaces Solution Approach
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