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Random Obstacle Problems : Ecole d'Ete de Probabilites de Saint-Flour XLV - 2015 - Lorenzo Zambotti

Random Obstacle Problems

Ecole d'Ete de Probabilites de Saint-Flour XLV - 2015

By: Lorenzo Zambotti

eText | 27 February 2017

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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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