BSDEs, weak convergence and homogenization of semilinear PDEs
BSDEs, weak convergence and homogenization of semilinear PDEs
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DOI：
10.1007/978-94-011-4560-2_9
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
É. Pardoux
中科院分区：
文献类型：
--
作者：
É. Pardoux
在这些讲座中，我们提出了向后随机微分方程的理论，以及它与抛物型和椭圆型半线性二阶偏微分方程的解的联系。这种联系为研究半线性偏微分方程的解提供了一种概率工具。我们应用我们的结果证明的均匀化结果，这样的偏微分方程，周期和随机系数。为此，我们需要提出倒向随机微分方程解的弱极限理论。我们还提出了一个完整的概率证明，显然是最小的假设下，线性二阶偏微分方程的均匀化结果。
In these lectures, we present the theory of backward stochastic differential equations, and its connection with solutions of semilinear second order partial differential equations of parabolic and elliptic type. This connection provides a probabilistic tool for studying solutions of semilinear PDEs. We apply our results to the proof of the homogenization result for such PDEs, both with periodic and random coefficients. For that purpose, we need to present the theory of weak limits of solutions of backward stochastic differential equations. We also present a complete probabilistic proof, under apparently minimal assumptions, of the homogenization result of linear second order PDEs.