论文信息 - Weak solution of semi-linear PDE, BSDE and homogenization - 字舞流文

Weak solution of semi-linear PDE, BSDE and homogenization

The sketch of the proof using BSDE of a homogenization result for semi-linear PDE with a divergence-form operator is given here. The method employed here relies on the use of a weak topology.

Antoine Lejay | A. Lejay

[1] A. Bensoussan,et al. Asymptotic analysis for periodic structures , 1979 .

[2] A. Lejay,et al. Méthodes probabilistes pour l'homogénéisation des opérateurs sous forme divergence : cas linéaires et semi-linéaires , 2000 .

[3] O. Ladyženskaja. Linear and Quasilinear Equations of Parabolic Type , 1968 .

[4] Ying Hu,et al. Stability of BSDEs with Random Terminal Time and Homogenization of Semilinear Elliptic PDEs , 1998 .

[5] A. Lejay. BSDE driven by Dirichlet process and semi-linear parabolic PDE. Application to homogenization , 2002 .

[6] Ali Süleyman Üstünel,et al. Stochastic Analysis and Related Topics II , 1993 .

[7] S. Peng,et al. Adapted solution of a backward stochastic differential equation , 1990 .

[8] Equations differentielles stochastiques retrogrades : applications aux equations aux derivees partielles , 1997 .

[9] Etienne Pardoux,et al. Homogenization of Linear and Semilinear Second Order Parabolic PDEs with Periodic Coefficients: A Probabilistic Approach☆ , 1999 .

[10] Homogenization of random semilinear PDEs , 2001 .

[11] N. Karoui,et al. Backward Stochastic Differential Equations , 1997 .

[12] Ying Hu,et al. Probabilistic approach to homogenization of viscosity solutions of parabolic PDEs , 1999 .

[13] Zhi-Ming Ma,et al. Introduction to the theory of (non-symmetric) Dirichlet forms , 1992 .

[14] É. Pardoux. BSDEs, weak convergence and homogenization of semilinear PDEs , 1999 .