Regularity of the density for the stochastic heat equation
Probability
2011-02-18 v1
Abstract
We study the smoothness of the density of a semilinear heat equation with multiplicative spacetime white noise. Using Malliavin calculus, we reduce the problem to a question of negative moments of solutions of a linear heat equation with multiplicative white noise. Then we settle this question by proving that solutions to the linear equation have negative moments of all orders.
Cite
@article{arxiv.0709.2663,
title = {Regularity of the density for the stochastic heat equation},
author = {Carl Mueller and David Nualart},
journal= {arXiv preprint arXiv:0709.2663},
year = {2011}
}