The heat equation with multiplicative stable L\'evy noise
Probability
2011-02-18 v1 Analysis of PDEs
Abstract
We study the heat equation with a random potential term. The potential is a one-sided stable noise, with positive jumps, which does not depend on time. To avoid singularities, we define the equation in terms of a construction similar to the Skorokhod integral or Wick product. We give a criterion for existence based on the dimension of the space variable, and the parameter p of the stable noise. Our arguments are different for p<1 and p>1.
Cite
@article{arxiv.math/0504027,
title = {The heat equation with multiplicative stable L\'evy noise},
author = {Carl Mueller and Leonid Mytnik and Aurel Stan},
journal= {arXiv preprint arXiv:math/0504027},
year = {2011}
}