THE OBSTACLE PROBLEM FOR QUASILINEAR STOCHASTIC PDES: ANALYTICAL APPROACH

被引：16

作者：

Denis, Laurent ^{[1
]}

Matoussi, Anis ^{[2
,3
]}

Zhang, Jing ^{[1
]}

机构：

[1] Univ Evry Val dEssonne, Lab Anal & Probabil, F-91037 Evry, France

[2] Univ Maine, Lab Manceau Math, Federat Rech 2962, CNRS Math Pays de Loire, F-72085 Le Mans 9, France

[3] Ecole Polytech, CMAP, Palaiseau, France

来源：

ANNALS OF PROBABILITY | 2014年 / 42卷 / 03期

关键词：

Parabolic potential; regular measure; stochastic partial differential equations; obstacle problem; penalization method; Ito's formula; comparison theorem; space time white noise; PARTIAL-DIFFERENTIAL-EQUATIONS; SPDES; REFLECTION;

D O I：

10.1214/12-AOP805

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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

引用

页码：865 / 905

页数：41

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