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A central limit theorem for the KPZ equation
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Hairer, Martin and Shen, Hao (2017) A central limit theorem for the KPZ equation. Annals of Probability, 45 (6B). pp. 4167-4221. doi:10.1214/16-AOP1162 ISSN 0091-1798.
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Official URL: http://doi.org/10.1214/16-AOP1162
Abstract
We consider a two-parameter averaging-homogenization type elliptic problem together with the stochastic representation of the solution. A limit theorem is derived for the corresponding diffusion process and a precise description of the two-parameter limit behavior for the solution of the PDE is obtained.We consider the KPZ equation in one space dimension driven by a stationary centred space-time random field, which is sufficiently integrable and mixing, but not necessarily Gaussian. We show that, in the weakly asymmetric regime, the solution to this equation considered at a suitable large scale and in a suitable reference frame converges to the Hopf-Cole solution to the KPZ equation driven by space-time Gaussian white noise. While the limiting process depends only on the integrated variance of the driving field, the diverging constants appearing in the definition of the reference frame also depend on higher order moments.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
Library of Congress Subject Headings (LCSH): | Stochastic partial differential equations, Differential equations, Partial, Distribution (Probability theory), Central limit theorem, Gaussian processes | |||||||||
Journal or Publication Title: | Annals of Probability | |||||||||
Publisher: | Institute of Mathematical Statistics | |||||||||
ISSN: | 0091-1798 | |||||||||
Official Date: | 12 December 2017 | |||||||||
Dates: |
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Volume: | 45 | |||||||||
Number: | 6B | |||||||||
Page Range: | pp. 4167-4221 | |||||||||
DOI: | 10.1214/16-AOP1162 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Date of first compliant deposit: | 13 October 2016 | |||||||||
Date of first compliant Open Access: | 19 April 2018 | |||||||||
RIOXX Funder/Project Grant: |
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