Moderate deviation for random elliptic PDE with small noise

Xiaoou Li, Jingchen Liu, Jianfeng Lu, Xiang Zhou

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)2781-2813
Number of pages33
JournalAnnals of Applied Probability
Issue number5
StatePublished - Oct 2018


  • Moderate deviation
  • Random partial differential equation
  • Rare event

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