Spatial asymptotics for the parabolic Anderson model driven by a Gaussian rough noise
Spatial asymptotics for the parabolic Anderson model driven by a Gaussian rough noise
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DOI：
10.1214/17-ejp83
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发表时间：
2016-07
期刊：
影响因子：
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通讯作者：
Xia Chen;Yaozhong Hu;D. Nualart;S. Tindel
中科院分区：
文献类型：
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作者：
Xia Chen;Yaozhong Hu;D. Nualart;S. Tindel
本文的目的是建立由时间为白色的高斯噪声驱动的一维空间随机热方程的解随空间变量变大时的几乎确定的渐近行为，该方程在空间变量中具有赫斯特参数大于1/4小于1/2的分数阶布朗运动协方差结构。
The aim of this paper is to establish the almost sure asymptotic behavior as the space variable becomes large, for the solution to the one spatial dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance structure of a fractional Brownian motion with Hurst parameter greater than 1/4 and less than 1/2 in the space variable.