LEADER 02799nam 22005055 450 001 996466769903316 005 20200702012029.0 010 $a3-319-52096-2 024 7 $a10.1007/978-3-319-52096-4 035 $a(CKB)3710000001080149 035 $a(DE-He213)978-3-319-52096-4 035 $a(MiAaPQ)EBC6280875 035 $a(MiAaPQ)EBC5576515 035 $a(Au-PeEL)EBL5576515 035 $a(OCoLC)1066194434 035 $a(PPN)198868421 035 $a(EXLCZ)993710000001080149 100 $a20170227d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRandom Obstacle Problems$b[electronic resource] $eÉcole d'Été de Probabilités de Saint-Flour XLV - 2015 /$fby Lorenzo Zambotti 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (IX, 162 p. 20 illus., 2 illus. in color.) 225 1 $aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v2181 311 $a3-319-52095-4 327 $a1 Introduction -- 2 The reflecting Brownian motion -- 3 Bessel processes -- 4 The stochastic heat equation -- 5 Obstacle problems -- 6 Integration by Parts Formulae -- 7 The contact set -- References. 330 $aStudying the fine properties of solutions to Stochastic (Partial) Differential Equations with reflection at a boundary, this book begins with a discussion of classical one-dimensional diffusions as the reflecting Brownian motion, devoting a chapter to Bessel processes, and moves on to function-valued solutions to SPDEs. Inspired by the classical stochastic calculus for diffusions, which is unfortunately still unavailable in infinite dimensions, it uses integration by parts formulae on convex sets of paths in order to describe the behaviour of the solutions at the boundary and the contact set between the solution and the obstacle. The text may serve as an introduction to space-time white noise, SPDEs and monotone gradient systems. Numerous open research problems in both classical and new topics are proposed. 410 0$aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v2181 606 $aProbabilities 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aProbabilities. 615 14$aProbability Theory and Stochastic Processes. 676 $a519.2 700 $aZambotti$b Lorenzo$4aut$4http://id.loc.gov/vocabulary/relators/aut$0739979 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466769903316 996 $aRandom obstacle problems$91466423 997 $aUNISA