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Moderate deviation for random elliptic PDE with small noise

Publication ,  Journal Article
Li, X; Liu, J; Lu, J; Zhou, X
Published in: Annals of Applied Probability
October 1, 2018

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.

Duke Scholars

Published In

Annals of Applied Probability

DOI

ISSN

1050-5164

Publication Date

October 1, 2018

Volume

28

Issue

5

Start / End Page

2781 / 2813

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4901 Applied mathematics
  • 0104 Statistics
  • 0102 Applied Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
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Li, X., Liu, J., Lu, J., & Zhou, X. (2018). Moderate deviation for random elliptic PDE with small noise. Annals of Applied Probability, 28(5), 2781–2813. https://doi.org/10.1214/17-AAP1373
Li, X., J. Liu, J. Lu, and X. Zhou. “Moderate deviation for random elliptic PDE with small noise.” Annals of Applied Probability 28, no. 5 (October 1, 2018): 2781–2813. https://doi.org/10.1214/17-AAP1373.
Li X, Liu J, Lu J, Zhou X. Moderate deviation for random elliptic PDE with small noise. Annals of Applied Probability. 2018 Oct 1;28(5):2781–813.
Li, X., et al. “Moderate deviation for random elliptic PDE with small noise.” Annals of Applied Probability, vol. 28, no. 5, Oct. 2018, pp. 2781–813. Scopus, doi:10.1214/17-AAP1373.
Li X, Liu J, Lu J, Zhou X. Moderate deviation for random elliptic PDE with small noise. Annals of Applied Probability. 2018 Oct 1;28(5):2781–2813.

Published In

Annals of Applied Probability

DOI

ISSN

1050-5164

Publication Date

October 1, 2018

Volume

28

Issue

5

Start / End Page

2781 / 2813

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4901 Applied mathematics
  • 0104 Statistics
  • 0102 Applied Mathematics