03381nam a22004575i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001600153072001600169072001700185072002300202072001500225072001600240100007800256245011400334250001800448264006900466300003200535336002600567337002600593338003600619347002400655490004600679505028900725520144301014650002602457650001402483650002502497700014102522710003402663773002602697776003602723776003602759776003602795830004602831856004602877978-3-031-69586-5DE-He21320251030112921.0cr nn 008mamaa240830s2024    sz |    s    |||| 0|eng d  a97830316958657 a10.1007/978-3-031-69586-52doi 4aQA274-274.9 7aPBT2bicssc 7aPBWL2bicssc 7aMAT0290002bisacsh 7aPBT2thema 7aPBWL2thema1 aGoodair, Daniel.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aStochastic Calculus in Infinite Dimensions and SPDEsh[electronic resource] /cby Daniel Goodair, Dan Crisan.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aX, 136 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringerBriefs in Mathematics,x2191-82010 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 .  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. . 0aStochastic processes. 0aCalculus.14aStochastic Calculus.1 aCrisan, Dan.eauthor.0(orcid)0000-0003-1486-15171https://orcid.org/0000-0003-1486-15174aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303169585808iPrinted edition:z978303169587208iPrinted edition:z9783031695889 0aSpringerBriefs in Mathematics,x2191-820140uhttps://doi.org/10.1007/978-3-031-69586-5