Large Deviation Theory for a Homogenized and "Corrected" Elliptic ODE
Analysis of PDEs
2010-12-07 v2
Abstract
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. These results allow one to access the limits of Gaussian correctors. In general, the corrector does not capture the large deviation behavior. Applications to uncertainty quantification are considered.
Cite
@article{arxiv.1012.0763,
title = {Large Deviation Theory for a Homogenized and "Corrected" Elliptic ODE},
author = {Guillaume Bal and Roger Ghanem and Ian Langmore},
journal= {arXiv preprint arXiv:1012.0763},
year = {2010}
}