02575nam a2200385 i 4500991003406789707536m o d cr |n|||||||||170801t20172017sz ob 100 0 eng d9783319520964electronic book3319520962electronic bookb14328896-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng519.2223LC QA274.25.Z36Zambotti, Lorenzo739979Random obstacle problems[e-book] :École d'Été de Probabilités de Saint-Flour XLV - 2015 /Lorenzo Zambotti[Cham], Switzerland :This Springer imprint is published by Springer Nature,[2017]©20171 online resource (ix, 164 pages)texttxtrdacontentcomputerrdamediaonline resourcerdacarrierLecture notes in mathematics,0075-8434 ;2181Includes bibliographical references1 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 ; ReferencesStudying 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 proposedStochastic partial differential equationsCongressesEcole d'été de probabilités de Saint-Flour<45th ;2015 ;Saint-Flour, France>https://link.springer.com/book/10.1007/978-3-319-52096-4An electronic book accessible through the World Wide.b1432889603-03-2201-08-17991003406789707536Random obstacle problems1466423UNISALENTOle01301-08-17m@ -engsz 00