English

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 H(14,12)H \in (\frac{1}{4}, \frac{1}{2}) 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 nnth moment of the solution.

Keywords

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

R2 v1 2026-06-22T17:28:52.653Z