Articles

JOINT HÖLDER CONTINUITY OF PARABOLIC ANDERSON MODEL

  • Yaozhong HU ,
  • Khoa LÊ
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  • 1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, T6G 2G1, Canada;
    2. Department of Mathematics, South Kensington Campus, Imperial College London, London, SW7 2AZ, United Kingdom

Received date: 2018-03-04

  Revised date: 2019-03-03

  Online published: 2019-06-27

Supported by

Y. Hu is supported by an NSERC grant and a startup fund of University of Alberta; K. Lê is supported by Martin Hairer's Leverhulme Trust leadership award.

Abstract

We obtain the Holder continuity and joint Holder continuity in space and time for the random field solution to the parabolic Anderson equation (t-1/2△)u=uW in d-dimensional space, where W is a mean zero Gaussian noise with temporal covariance γ0 and spatial covariance given by a spectral density μ(ξ). We assume that γ0(t) ≤ c|t|-α0 and |μ(ξ)| ≤ c|ξi|-αi or |μ(ξ)| ≤ c|ξ|-α, where αi, i=1,…, d (or α) can take negative value.

Cite this article

Yaozhong HU , Khoa LÊ . JOINT HÖLDER CONTINUITY OF PARABOLIC ANDERSON MODEL[J]. Acta mathematica scientia, Series B, 2019 , 39(3) : 764 -780 . DOI: 10.1007/s10473-019-0309-0

References

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