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Stochastic heat equation driven by fractional noise and local time

被引：102
|
作者：
Hu, Yaozhong [1 ]
Nualart, David [1 ]
机构：
[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA
来源：
PROBABILITY THEORY AND RELATED FIELDS | 2009年 / 143卷 / 1-2期
基金：
美国国家科学基金会;
关键词：
EVOLUTION-EQUATIONS; INTEGRALS;
D O I：
10.1007/s00440-007-0127-5
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
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 is an element of (0,1) in time. Two types of equations are considered. First we consider the equation in the Ito-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：44
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