Random obstacle problems: école d'été de probabilités de Saint-Flour XLV - 2015 / Lorenzo Zambotti

Collectivité principale: école d'été de probabilités de Saint-Flour, 45, Saint-Flour (2015) Co-auteur: Zambotti, Lorenzo (1973-) - AuteurType de document: CongrèsCollection: Lecture notes in mathematics, école d'été de probabilités de Saint-Flour ; 2181Langue: anglaisPays: SwisseÉditeur: Cham : Springer, 2017Description: 1 vol. (IX-162 p.) : fig. ; 24 cm ISBN: 9783319520957 ; br. Résumé: Publisher’s description: Studying 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..Bibliographie: Bibliogr. p. 159-162. Sujets MSC: 60-02 Probability theory and stochastic processes -- Research exposition (monographs, survey articles)
60J65 Probability theory and stochastic processes -- Markov processes -- Brownian motion
60G07 Probability theory and stochastic processes -- Stochastic processes -- General theory of processes
60H15 Probability theory and stochastic processes -- Stochastic analysis -- Stochastic partial differential equations
35K86 Partial differential equations -- Parabolic equations and systems -- Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities
En-ligne: Springerlink - résumé | zbMath | MSN

Bibliogr. p. 159-162

Publisher’s description: Studying 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.

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