The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 28, Number 5 (2018), 2781-2813.
Moderate deviation for random elliptic PDE with small noise
Partial differential equations with random inputs have become popular models to characterize physical systems with uncertainty coming from imprecise measurement and intrinsic randomness. In this paper, we perform asymptotic rare-event analysis for such elliptic PDEs with random inputs. In particular, we consider the asymptotic regime that the noise level converges to zero suggesting that the system uncertainty is low, but does exist. We develop sharp approximations of the probability of a large class of rare events.
Ann. Appl. Probab., Volume 28, Number 5 (2018), 2781-2813.
Received: October 2016
Revised: November 2017
First available in Project Euclid: 28 August 2018
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Li, Xiaoou; Liu, Jingchen; Lu, Jianfeng; Zhou, Xiang. Moderate deviation for random elliptic PDE with small noise. Ann. Appl. Probab. 28 (2018), no. 5, 2781--2813. doi:10.1214/17-AAP1373. https://projecteuclid.org/euclid.aoap/1535443234