LEADER 03223nam 22005055 450 001 9910886081203321 005 20250630193209.0 010 $a3-031-69586-0 024 7 $a10.1007/978-3-031-69586-5 035 $a(MiAaPQ)EBC31626776 035 $a(Au-PeEL)EBL31626776 035 $a(CKB)34512638500041 035 $a(DE-He213)978-3-031-69586-5 035 $a(EXLCZ)9934512638500041 100 $a20240830d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStochastic Calculus in Infinite Dimensions and SPDEs /$fby Daniel Goodair, Dan Crisan 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (143 pages) 225 1 $aSpringerBriefs in Mathematics,$x2191-8201 311 08$a3-031-69585-2 327 $a1 Introduction -- 2 Stochastic Calculus in Infinite Dimensions -- 3 Stochastic Differential Equations in Infinite Dimensions -- 4 A Toolbox for Nonlinear SPDEs -- 5 Existence Theory for Nonlinear SPDEs and the Stochastic Navier-Stokes Equations -- A Appendix -- References -- Index . 330 $aIntroducing a groundbreaking framework for stochastic partial differential equations (SPDEs), this work presents three significant advancements over the traditional variational approach. Firstly, Stratonovich SPDEs are explicitly addressed. Widely used in physics, Stratonovich SPDEs have typically been converted to Ito form for mathematical treatment. While this conversion is understood heuristically, a comprehensive treatment in infinite dimensions has been lacking, primarily due to insufficient rigorous results on martingale properties. Secondly, the framework incorporates differential noise, assuming the noise operator is only bounded from a smaller Hilbert space into a larger one, rather than within the same space. This necessitates additional regularity in the Ito form to solve the original Stratonovich SPDE. This aspect has been largely overlooked, despite the increasing popularity of gradient-dependent Stratonovich noise in fluid dynamics and regularisation by noise studies. Lastly, the framework departs from the explicit duality structure (Gelfand Triple), which is typically expected in the study of analytically strong solutions. This extension builds on the classical variational framework established by Röckner and Pardoux, advancing it in all three key aspects. Explore this innovative approach that not only addresses existing challenges but also opens new avenues for research and application in SPDEs. . 410 0$aSpringerBriefs in Mathematics,$x2191-8201 606 $aStochastic processes 606 $aCalculus 606 $aStochastic Calculus 615 0$aStochastic processes. 615 0$aCalculus. 615 14$aStochastic Calculus. 676 $a519.23 700 $aGoodair$b Daniel$01770560 701 $aCrisan$b Dan$0524271 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910886081203321 996 $aStochastic Calculus in Infinite Dimensions and SPDEs$94252788 997 $aUNINA