Description du livre
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About this book
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.
Written for:
Researchers and graduate students in mathematics, physics and economics
Keywords:
Yamada-Watanabe theorem
invariant measures
stochastic integrals in Hilbert space
stochastic partial differential equations
variational approach "