Parabolic Anderson model with rough dependence in space
Probability
2016-12-21 v1
Abstract
This paper studies the one-dimensional parabolic Anderson model driven by a Gaussian noise which is white in time and has the covariance of a fractional Brownian motion with Hurst parameter in the space variable. We derive the Wiener chaos expansion of the solution and a Feynman-Kac formula for the moments of the solution. These results allow us to establish sharp lower and upper asymptotic bounds for the th moment of the solution.
Cite
@article{arxiv.1612.06437,
title = {Parabolic Anderson model with rough dependence in space},
author = {Yaozhong Hu and Jingyu Huang and Khoa Lê and David Nualart and Samy Tindel},
journal= {arXiv preprint arXiv:1612.06437},
year = {2016}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1505.04924