Stochastic Heat Equation Driven by Fractional Noise and Local Time

Details Stochastic Heat Equation Driven by Fractional Noise and Local Time Stochastic Heat Equation Driven by Fractional Noise and Local Time

2007-04-13

arxiv.org/abs/0704.1824v1

Mathematics

Probability

Scientific paper

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 it has the covariance of a fractional Brownian motion with Hurst parameter $% H\in (0,1)$ 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.

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