Stability of BSDEs with Random Terminal Time and Homogenization of Semilinear Elliptic PDEs
Stability of BSDEs with Random Terminal Time and Homogenization of Semilinear Elliptic PDEs
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DOI：
10.1006/jfan.1997.3229
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发表时间：
1998-06
影响因子：
1.7
通讯作者：
P. Briand;Ying Hu
中科院分区：
文献类型：
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作者：
P. Briand;Ying Hu
在本文中，我们推广的概率方法均匀化的半线性抛物型偏微分方程，开发的Buckdahn，胡，和彭的情况下，椭圆型偏微分方程。首先，我们给出了具有随机终端时间的倒向随机微分方程的稳定性结果，这些结果与Peng（Stochastics Stochastics Rep.37（1991），61-74）中所示的椭圆型偏微分方程有关。在一维情况下，我们也部分放松了对系数的单调性假设。然后，我们使用这些稳定性的结果与随机终端时间的BSDES研究均匀化的半线性椭圆型偏微分方程系统。
In this paper, we extend the probabilistic method for homogenization of semi-linear parabolic PDEs, developed by Buckdahn, Hu, and Peng to the case of elliptic PDEs. First, we give a stability result for BSDEs with random terminal time which are related to elliptic PDEs as shown in Peng (Stochastics Stochastics Rep.37(1991), 61–74). In the one dimensional case, we also partially relax the monotonicity assumption on the coefficient. Then, we use these stability results for BSDEs with random terminal time to study homogenization of systems of semilinear elliptic PDEs.