Random obstacle problems : École d'Été de Probabilités de Saint-Flour XLV - 2015 / Lorenzo Zambotti.

Format:

Book

Conference/Event

Author/Creator:

Zambotti, Lorenzo, author.

Conference Name:

Ecole d'été de probabilités de Saint-Flour (45th : 2015 : Saint-Flour, France), creator.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 2181.

Lecture notes in mathematics (Springer-Verlag). École d'été de probabilités de Saint-Flour

Lecture notes in mathematics, 0075-8434 ; 2181. École d'Été de Probabilités de Saint-Flour, 0721-5363

Language:

English

Subjects (All):

Stochastic partial differential equations--Congresses.

Stochastic partial differential equations.

Genre:

Conference papers and proceedings.

Physical Description:

ix, 162 pages : illustrations ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer, [2017]

Summary:

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.

Contents:

Introduction

The reflecting Brownian motion

Bessel processes

The stochastic heat equation

Obstacle problems

Integration by Parts Formulae

The contact set.

Notes:

Includes bibliographical references.

ISBN:

9783319520957

3319520954

OCLC:

966183518

Publisher Number:

9783319520957