The obstacle problem for quasilinear stochastic PDEs: Analytical approach

Laurent Denis; Anis Matoussi; Jing Zhang

doi:10.1214/12-AOP805

The obstacle problem for quasilinear stochastic PDEs: Analytical approach

Probability 2014-03-28 v2

Authors: Laurent Denis , Anis Matoussi , Jing Zhang

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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 $(u,\nu)$ where $u$ is a predictable continuous process which takes values in a proper Sobolev space and $\nu$ is a random regular measure satisfying the minimal Skohorod condition.

Keywords

stochastic differential equations partial differential equations

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@article{arxiv.1202.3296,
  title  = {The obstacle problem for quasilinear stochastic PDEs: Analytical approach},
  author = {Laurent Denis and Anis Matoussi and Jing Zhang},
  journal= {arXiv preprint arXiv:1202.3296},
  year   = {2014}
}

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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)

The obstacle problem for quasilinear stochastic PDEs: Analytical approach

Abstract

Keywords

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