Large deviation theory for a homogenized and corrected elliptic ODE

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:251

Article

Bal, Guillaume¹  Ghanem, Roger²  Langmore, Ian¹ 

[1] Columbia Univ, Dept Appl Phys & Appl Math, New York, NY 10027 USA

[2] Univ So Calif, Los Angeles, CA 90089 USA

关键词: Differential equations;    Probability theory;    Random coefficients;    Homogenization;    Applied mathematics;    Uncertainty quantification;   

DOI  :  10.1016/j.jde.2011.04.026

来源: Elsevier

【 摘 要 】

We study a one-dimensional elliptic problem with highly oscillatory random diffusion coefficient. We derive a homogenized solution and a so-called Gaussian corrector. We also prove a pointwise large deviation principle (LDP) for the full solution and approximate this LDP with a more tractable form. Applications to uncertainty quantification are considered. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free