MODERATE DEVIATION FOR RANDOM ELLIPTIC PDE WITH SMALL NOISE

• 成果类型: Article
• 署名作者: Li, Xiaoou; Liu, Jingchen; Lu, Jianfeng; Zhou, Xiang
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Columbia University; Duke University; Duke University; City University of Hong Kong
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1373
• 发表日期: 2018
• 页码: 2781-2813
• 关键词: tail probabilities; random-fields; maximum

摘要

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.