Homogenization of Linear and Semilinear Second Order Parabolic PDEs with Periodic Coefficients: A Probabilistic Approach☆
Homogenization of Linear and Semilinear Second Order Parabolic PDEs with Periodic Coefficients: A Probabilistic Approach☆
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DOI：
10.1006/jfan.1999.3441
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发表时间：
1999-10
影响因子：
1.7
通讯作者：
É. Pardoux
中科院分区：
文献类型：
--
作者：
É. Pardoux
研究了具有快速振荡周期系数、奇异漂移和零阶项奇异系数的线性和半线性二阶抛物型偏微分方程解的极限。我们的证明方法是完全概率的，并建立在早期工作的论点。在线性情况下，我们使用Feynman Kac公式来表示抛物型偏微分方程的解，在半线性情况下，我们使用一个相关的倒向随机微分方程。
We study the limit of the solution of linear and semilinear second order PDEs of parabolic type, with rapidly oscillating periodic coefficients, singular drift, and singular coefficient of the zeroth order term. Our method of proof is fully probabilistic and builds upon the arguments in earlier work. In the linear case, we use the Feynman Kac formula to represent the solution of the parabolic PDE, and in the semilinear case we use an associated backward stochastic differential equation.