均匀化和“修正”椭圆ODE的大偏差理论
Large Deviation Theory for a Homogenized and "Corrected" Elliptic ODE
摘要：
研究了具有高振荡随机扩散系数的一维椭圆问题。我们得到一个均匀化的解决方案和所谓的高斯校正。我们还证明了一个“逐点”大偏差原则（LDP）的完整的解决方案，并近似此LDP更容易处理的形式。这些结果允许人们访问高斯校正器的限制。通常，校正器不捕获大偏差行为。被认为是不确定性量化的应用。
英文摘要：
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. 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.
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