A Central Limit Theorem for the KPZ Equation

Martin Hairer Imperial College Hao Shen Columbia University

Probability mathscidoc:1805.28005

The Annals of Probability, 45, (6), 4167–4221, 2017
We consider the KPZ equation in one space dimension driven by a sta- tionary 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 limit- ing 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.
Stochastic PDE, regularity structure, KPZ equation
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@inproceedings{martin2017a,
  title={A Central Limit Theorem for the KPZ Equation},
  author={Martin Hairer, and Hao Shen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180530085500482825092},
  booktitle={The Annals of Probability},
  volume={45},
  number={6},
  pages={4167–4221},
  year={2017},
}
Martin Hairer, and Hao Shen. A Central Limit Theorem for the KPZ Equation. 2017. Vol. 45. In The Annals of Probability. pp.4167–4221. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180530085500482825092.
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