Auxiliary SDEs for homogenization of quasilinear PDEs with periodic coefficients

• 成果类型: Article
• 署名作者: Delarue, F
• 署名单位: Universite Paris Cite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000144
• 发表日期: 2004
• 页码: 2305-2361
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; parabolic PDEs; probabilistic approach; diffusion-approximation; VISCOSITY SOLUTIONS; Poisson equation; bsde

摘要

We study the homogenization property of systems of quasi-linear PDEs of parabolic type with periodic coefficients, highly oscillating drift and highly oscillating nonlinear term. To this end, we propose a probabilistic approach based on the theory of forward-backward stochastic differential equations and introduce the new concept of auxiliary SDEs.