Homogenization of random semilinear PDEs

• 成果类型: Article
• 署名作者: Castell, F
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400100164
• 发表日期: 2001
• 页码: 492-524
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; reversible markov-processes; invariance-principle; WEAK-CONVERGENCE; STABILITY; THEOREM; BSDEs; time

摘要

We prove a homogenization result for system of semilinear parabolic PDEs of the type partial derivative(t)u(epsilon) = (1)/(2)e(2V(x/epsilon)) div (e(-2V(x/epsilon)) a(x/epsilon)delu(epsilon)) + h(x,u(epsilon), delu(epsilon)). where V and a are random ergodic fields. We extend to the random case, results of Buck-dahn, Hu & Peng [4] for periodic structures. The same method involving stability results is applied. Our main tool is an L-p estimate for the gradient of the solution of the auxiliary problems. The same type of results is obtained for systems of semilinear elliptic PDEs.