LEADER 03000nam 22005415 450 001 9910506397303321 005 20251113190739.0 010 $a3-030-89003-1 024 7 $a10.1007/978-3-030-89003-2 035 $a(CKB)5340000000068442 035 $a(MiAaPQ)EBC6792424 035 $a(Au-PeEL)EBL6792424 035 $a(OCoLC)1280603279 035 $a(PPN)258298200 035 $a(DE-He213)978-3-030-89003-2 035 $a(EXLCZ)995340000000068442 100 $a20211025d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStochastic Partial Differential Equations $eAn Introduction /$fby Étienne Pardoux 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (78 pages) 225 1 $aSpringerBriefs in Mathematics,$x2191-8201 311 08$a3-030-89002-3 327 $a-1. Introduction and Motivation -- 2. SPDEs as Infinite-Dimensional SDEs -- 3. SPDEs Driven By Space-Time White Noise -- References -- Index. 330 $aThis book gives a concise introduction to the classical theory of stochastic partial differential equations (SPDEs). It begins by describing the classes of equations which are studied later in the book, together with a list of motivating examples of SPDEs which are used in physics, population dynamics, neurophysiology, finance and signal processing. The central part of the book studies SPDEs as infinite-dimensional SDEs, based on the variational approach to PDEs. This extends both the classical Itô formulation and the martingale problem approach due to Stroock and Varadhan. The final chapter considers the solution of a space-time white noise-driven SPDE as a real-valued function of time and (one-dimensional) space. The results of J. Walsh's St Flour notes on the existence, uniqueness and Hölder regularity of the solution are presented. In addition, conditions are given under which the solution remains nonnegative, and the Malliavin calculus is applied. Lastly, reflected SPDEs and theirconnection with super Brownian motion are considered. At a time when new sophisticated branches of the subject are being developed, this book will be a welcome reference on classical SPDEs for newcomers to the theory. 410 0$aSpringerBriefs in Mathematics,$x2191-8201 606 $aStochastic analysis 606 $aDifferential equations 606 $aStochastic Analysis 606 $aDifferential Equations 615 0$aStochastic analysis. 615 0$aDifferential equations. 615 14$aStochastic Analysis. 615 24$aDifferential Equations. 676 $a519.2 700 $aPardoux$b E$g(Etienne),$f1947-$0421970 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910506397303321 996 $aStochastic Partial Differential Equations$92569210 997 $aUNINA