• 论文 •

### JOINT HÖLDER CONTINUITY OF PARABOLIC ANDERSON MODEL

1. 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
• 收稿日期:2018-03-04 修回日期:2019-03-03 出版日期:2019-06-25 发布日期:2019-06-27
• 作者简介:Yaozhong HU,E-mail:yaozhong@ualberta.ca;Khoa LÊ,E-mail:n.le@imperial.ac.uk
• 基金资助:
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.

### JOINT HÖLDER CONTINUITY OF PARABOLIC ANDERSON MODEL

Yaozhong HU1, Khoa LÊ2

1. 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:2018-03-04 Revised:2019-03-03 Online:2019-06-25 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.

• 60H15