LEADER 03339nam 2200613 450 001 9910482992803321 005 20220223133256.0 010 $a1-280-90216-7 010 $a9786610902163 010 $a3-540-70781-6 024 7 $a10.1007/978-3-540-70781-3 035 $a(CKB)1000000000282697 035 $a(EBL)3036683 035 $a(SSID)ssj0000292401 035 $a(PQKBManifestationID)11228980 035 $a(PQKBTitleCode)TC0000292401 035 $a(PQKBWorkID)10269160 035 $a(PQKB)11385217 035 $a(DE-He213)978-3-540-70781-3 035 $a(MiAaPQ)EBC3036683 035 $a(MiAaPQ)EBC6857963 035 $a(Au-PeEL)EBL6857963 035 $a(PPN)123160049 035 $a(EXLCZ)991000000000282697 100 $a20220223d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 12$aA concise course on stochastic partial differential equations /$fClaudia Pre?vo?t, Michael Ro?ckner 205 $a1st ed. 2007. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer,$d[2007] 210 4$dİ2007 215 $a1 online resource (148 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1905 300 $aDescription based upon print version of record. 311 $a3-540-70780-8 320 $aIncludes bibliographical references (p. 137-139) and index. 327 $aMotivation, 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. 330 $aThese lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. To keep the technicalities minimal we confine ourselves to the case where the noise term is given by a stochastic integral w.r.t. a cylindrical Wiener process.But all results can be easily generalized to SPDE with more general noises such as, for instance, stochastic integral w.r.t. a continuous local martingale. There are basically three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material, such as definitions and results from the theory of Hilbert spaces, are included in appendices. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1905 606 $aStochastic differential equations 615 0$aStochastic differential equations. 676 $a519.2 700 $aPre?vo?t$b Claudia$0472505 702 $aRo?ckner$b Michael$f1956- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910482992803321 996 $aA Concise Course on Stochastic Partial Differential Equations$92585735 997 $aUNINA