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November 2017 A central limit theorem for the KPZ equation
Martin Hairer, Hao Shen
Ann. Probab. 45(6B): 4167-4221 (November 2017). DOI: 10.1214/16-AOP1162


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.


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Martin Hairer. Hao Shen. "A central limit theorem for the KPZ equation." Ann. Probab. 45 (6B) 4167 - 4221, November 2017.


Received: 1 July 2015; Revised: 1 August 2016; Published: November 2017
First available in Project Euclid: 12 December 2017

zbMATH: 06838118
MathSciNet: MR3737909
Digital Object Identifier: 10.1214/16-AOP1162

Primary: 60H15
Secondary: 35K55 , 60H30

Keywords: central limit theorem , Cumulants , KPZ equation , Wiener Chaos

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.45 • No. 6B • November 2017
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