TY  - BOOK
AU  - Zambotti,Lorenzo
ED  - SpringerLink (Online service)
TI  - Random Obstacle Problems: École d'Été de Probabilités de Saint-Flour XLV - 2015 
T2  - École d'Été de Probabilités de Saint-Flour,
SN  - 9783319520964
AV  - QA273.A1-274.9 
U1  - 519.2 23
PY  - 2017///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Distribution (Probability theory
KW  - Probability Theory and Stochastic Processes
N1  - 1 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-319-52096-4
ER  -