03339nam 2200613 450 991048299280332120220223133256.01-280-90216-797866109021633-540-70781-610.1007/978-3-540-70781-3(CKB)1000000000282697(EBL)3036683(SSID)ssj0000292401(PQKBManifestationID)11228980(PQKBTitleCode)TC0000292401(PQKBWorkID)10269160(PQKB)11385217(DE-He213)978-3-540-70781-3(MiAaPQ)EBC3036683(MiAaPQ)EBC6857963(Au-PeEL)EBL6857963(PPN)123160049(EXLCZ)99100000000028269720220223d2007 uy 0engur|n|---|||||txtccrA concise course on stochastic partial differential equations /Claudia Prévôt, Michael Röckner1st ed. 2007.Berlin, Germany ;New York, New York :Springer,[2007]©20071 online resource (148 p.)Lecture Notes in Mathematics,0075-8434 ;1905Description based upon print version of record.3-540-70780-8 Includes bibliographical references (p. 137-139) and index.Motivation, Aims and Examples -- Stochastic Integral in Hilbert spaces -- Stochastic Differential Equations in Finite Dimensions -- A Class of Stochastic Differential Equations in Banach Spaces -- Appendices: The Bochner Integral -- Nuclear and Hilbert-Schmidt Operators -- Pseudo Invers of Linear Operators -- Some Tools from Real Martingale Theory -- Weak and Strong Solutions: the Yamada-Watanabe Theorem -- Strong, Mild and Weak Solutions.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.Lecture Notes in Mathematics,0075-8434 ;1905Stochastic differential equationsStochastic differential equations.519.2Prévôt Claudia472505Röckner Michael1956-MiAaPQMiAaPQMiAaPQBOOK9910482992803321A Concise Course on Stochastic Partial Differential Equations2585735UNINA