Stochastic heat equation driven by fractional noise and local time

被引：5
|
作者：
Yaozhong Hu
David Nualart
机构：
[1] University of Kansas,Department of Mathematics
来源：
Probability Theory and Related Fields | 2009年 / 143卷
关键词：
60H15; 60H07;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The aim of this paper is to study the d-dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and has the covariance of a fractional Brownian motion with Hurst parameter H ∈ (0,1) in time. Two types of equations are considered. First we consider the equation in the Itô-Skorohod sense, and later in the Stratonovich sense. An explicit chaos expansion for the solution is obtained. On the other hand, the moments of the solution are expressed in terms of the exponential moments of some weighted intersection local time of the Brownian motion.
引用
收藏
页码：285 / 328
页数：43
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