Stochastic heat equation driven by fractional noise and local time

• 成果类型: Article
• 署名作者: Hu, Yaozhong; Nualart, David
• 署名单位: University of Kansas
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-007-0127-5
• 发表日期: 2009
• 页码: 285-328
• 关键词: evolution-equations; INTEGRALS

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.