On the large-scale structure of the tall peaks for stochastic heat equations with fractional Laplacian
On the large-scale structure of the tall peaks for stochastic heat equations with fractional Laplacian
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分数拉普拉斯随机热方程高峰的大尺度结构
DOI：
10.1016/j.spa.2018.07.006
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发表时间：
2015
影响因子：
1.4
通讯作者：
Kunwoo Kim
中科院分区：
文献类型：
--
作者：
Kunwoo Kim
考虑Rd上具有分数阶Laplacian算子的随机热方程.驱动噪声是广义高斯噪声，它在时间上是白色的，但在空间上是均匀的。我们研究了线性随机热方程和抛物型安德森模型的高峰的大尺度结构。我们获得了峰的最大阶数，并计算了（i）和（ii）峰的宏观豪斯多夫维度。这些结果表明，（i）和（ii）都表现出多重分形行为，即使只有（ii）是间歇性的。这是Khoshnevisan等人的一个结果的推广。（2017）到更广泛的一类随机热方程。
Consider stochastic heat equations with fractional Laplacian on R d. The driving noise is generalized Gaussian which is white in time but spatially homogeneous. We study the large-scale structure of the tall peaks for (i) the linear stochastic heat equation and (ii) the parabolic Anderson model. We obtain the largest order of the peaks and compute the macroscopic Hausdorff dimensions of the peaks for (i) and (ii). These result imply that both (i) and (ii) exhibit multi-fractal behavior even though only (ii) is intermittent. This is an extension of a result of Khoshnevisan et al.(2017) to a wider class of stochastic heat equations.