Fluctuations of parabolic equations with large random potentials
作者： Yu Gu , Guillaume Bal
DOI: 10.1007/S40072-014-0040-8
关键词: Martingale (probability theory) 、 Mathematics 、 Asymptotic distribution 、 Martingale central limit theorem 、 Numerical analysis 、 Parabolic partial differential equation 、 Partial differential equation 、 Weak convergence 、 Homogenization (chemistry) 、 Mathematical analysis
摘要: In this paper, we present a fluctuation analysis of type parabolic equations with large, highly oscillatory, random potentials around the homogenization limit. With Feynman–Kac representation, Kipnis–Varadhan’s method, and quantitative martingale central limit theorem, derive asymptotic distribution rescaled error between heterogeneous homogenized solutions under different assumptions in dimension \(d\ge 3\). The results depend on whether stationary corrector exits.
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