The obstacle problem for quasilinear stochastic PDEs: Analytical approach

2012/02/29 by Laurent Denis, Anis Matoussi, Jing Zhang · 2 citations
Mathematics · #math.PR

paper · pdf · doi:10.1214/12-aop805

published as Annals of Probability 2014, Vol. 42, No. 3, 865-905 · Published in at http://dx.doi.org/10.1214/12-AOP805 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

arxiv created 2014/03/27 · arxiv updated 2014/03/28

Abstract

We prove an existence and uniqueness result for quasilinear Stochastic PDEs with obstacle (OSPDE in short). Our method is based on analytical technics coming from the parabolic potential theory. The solution is expressed as a pair (u,ν) where u is a predictable continuous process which takes values in a proper Sobolev space and ν is a random regular measure satisfying the minimal Skohorod condition.

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• The Obstacle Problem for Quasilinear Stochastic PDEs with Neumann boundary condition

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