Stochastic Heat Equation Driven by Fractional Noise and Local Time
Probability
2007-05-23 v1 Analysis of PDEs
Abstract
The aim of this paper is to study the -dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and it has the covariance of a fractional Brownian motion with Hurst parameter in time. Two types of equations are considered. First we consider the equation in the It\^{o}-Skorohod sense, and later in the Stratonovich sense. An explicit chaos development 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.
Keywords
Cite
@article{arxiv.0704.1824,
title = {Stochastic Heat Equation Driven by Fractional Noise and Local Time},
author = {Yaozhong Hu and David Nualart},
journal= {arXiv preprint arXiv:0704.1824},
year = {2007}
}