Reflected BSDEs and the obstacle problem for semilinear PDEs in divergence form

被引：17

作者：

Klimsiak, Tomasz ^{[1
]}

机构：

[1] Nicolaus Copernicus Univ, Fac Math & Comp Sci, PL-87100 Torun, Poland

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2012年 / 122卷 / 01期

关键词：

Backward stochastic differential equation; Semilinear parabolic partial differential equation; Divergence form operator; Obstacle problem; Weak solution; Soft measure; PARABOLIC CAPACITY; WEAK SOLUTIONS; BACKWARD SDES; EXISTENCE; EQUATIONS; UNIQUENESS; EVOLUTION;

D O I：

10.1016/j.spa.2011.10.001

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 consider the Cauchy problem for a semilinear parabolic equation in divergence form with obstacle. We show that under natural conditions on the right-hand side of the equation and mild conditions on the obstacle, the problem has a unique solution and we provide its stochastic representation in terms of reflected backward stochastic differential equations. We also prove regularity properties and approximation results for solutions of the problem. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：134 / 169

页数：36

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