Feynman-Kac formula for heat equation driven by fractional white noise
Abstract
We establish a version of the Feynman-Kac formula for the multidimensional stochastic heat equation with a multiplicative fractional Brownian sheet. We use the techniques of Malliavin calculus to prove that the process defined by the Feynman-Kac formula is a weak solution of the stochastic heat equation. From the Feynman-Kac formula, we establish the smoothness of the density of the solution and the H\"{o}lder regularity in the space and time variables. We also derive a Feynman-Kac formula for the stochastic heat equation in the Skorokhod sense and we obtain the Wiener chaos expansion of the solution.
Keywords
Cite
@article{arxiv.0906.3076,
title = {Feynman-Kac formula for heat equation driven by fractional white noise},
author = {Yaozhong Hu and David Nualart and Jian Song},
journal= {arXiv preprint arXiv:0906.3076},
year = {2010}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AOP547 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)