Random Obstacle Problems: cole d't de Probabilits de Saint-Flour XLV - 2015 [Paperback]

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.

This book is an excellent, rigorous monograph on stochastic partial differential equations with reflections at a boundary. & Engineers who struggle with numerical solutions of heat equations and Fokker-Plank equations in phase lock theory in white and colored noise will find this book useful. The author is a leading contributor to this field and has noted several open problems (Nirode C. Mohanty, zbMATH 1386.60002, 2018)

Studying the fine properties of solutions to Stochastic (Partial) Differential Equations with rl#m