The Annals of Applied Probability

Moderate deviation for random elliptic PDE with small noise

Xiaoou Li, Jingchen Liu, Jianfeng Lu, and Xiang Zhou

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 28, Number 5 (2018), 2781-2813.

Dates
Received: October 2016
Revised: November 2017
First available in Project Euclid: 28 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1535443234

Digital Object Identifier
doi:10.1214/17-AAP1373

Mathematical Reviews number (MathSciNet)
MR3847973

Zentralblatt MATH identifier
06974765

Subjects
Primary: 60F10: Large deviations 60Z05
Secondary: 60G15: Gaussian processes

Keywords
Random partial differential equation rare event moderate deviation

Citation

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


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