文章基本信息

标题：On the intermittency front of stochastic heat equation driven by colored noises
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作者：Yaozhong Hu ; Jingyu Huang ; David Nualart 等
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2016
卷号：21
DOI：10.1214/16-ECP4364
语种：English
出版社：Electronic Communications in Probability
摘要：We study the propagation of high peaks (intermittency fronts) of the solution to a stochastic heat equation driven by multiplicative centered Gaussian noise in $\mathbb{R} ^d$. The noise is assumed to have a general homogeneous covariance in both time and space, and the solution is interpreted in the senses of the Wick product. We give some estimates for the upper and lower bounds of the propagation speed, based on a moment formula of the solution. When the space covariance is given by a Riesz kernel, we give more precise bounds for the propagation speed.
关键词：stochastic heat equation;Feynman-Kac formula;intermittency front;Malliavin calculus;comparison principle.