The Annals of Probability

The obstacle problem for quasilinear stochastic PDEs: Analytical approach

Laurent Denis, Anis Matoussi, and Jing Zhang

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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.

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Ann. Probab. Volume 42, Number 3 (2014), 865-905.

First available in Project Euclid: 26 March 2014

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Primary: 60H15: Stochastic partial differential equations [See also 35R60] 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 31B150

Parabolic potential regular measure stochastic partial differential equations obstacle problem penalization method Itô’s formula comparison theorem space–time white noise


Denis, Laurent; Matoussi, Anis; Zhang, Jing. The obstacle problem for quasilinear stochastic PDEs: Analytical approach. Ann. Probab. 42 (2014), no. 3, 865--905. doi:10.1214/12-AOP805.

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