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October 2018 Moderate deviation for random elliptic PDE with small noise
Xiaoou Li, Jingchen Liu, Jianfeng Lu, Xiang Zhou
Ann. Appl. Probab. 28(5): 2781-2813 (October 2018). DOI: 10.1214/17-AAP1373

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.

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Xiaoou Li. Jingchen Liu. Jianfeng Lu. Xiang Zhou. "Moderate deviation for random elliptic PDE with small noise." Ann. Appl. Probab. 28 (5) 2781 - 2813, October 2018. https://doi.org/10.1214/17-AAP1373

Information

Received: 1 October 2016; Revised: 1 November 2017; Published: October 2018
First available in Project Euclid: 28 August 2018

zbMATH: 06974765
MathSciNet: MR3847973
Digital Object Identifier: 10.1214/17-AAP1373

Subjects:
Primary: 60F10 , 60Z05
Secondary: 60G15

Keywords: Moderate deviation , Random partial differential equation , Rare event

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.28 • No. 5 • October 2018
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