Large deviation theory for a homogenized and “corrected” elliptic ODE |
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| Authors: | Guillaume Bal Ian Langmore |
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| Institution: | a Department of Applied Physics and Applied Mathematics, Columbia University, United States
b University of Southern California, United States |
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| 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. Applications to uncertainty quantification are considered. |
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| Keywords: | Differential equations Probability theory Random coefficients Homogenization Applied mathematics Uncertainty quantification |
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