-4. chen.huang:19:regularity#
Regularity and strict positivity of densities for the stochastic heat equation on \(\mathbb{R}^d\)
Le Chen and Jingyu Huang
Abstract: In this paper, we study the stochastic heat equation with a general multiplicative Gaussian noise that is white in time and colored in space. Both regularity and strict positivity of the densities of the solution have been established. The difficulty, and hence the contribution, of the paper lie in three aspects: rough initial conditions, degenerate diffusion coefficient, and weakest possible assumptions on the correlation function of the noise. In particular, our results cover the parabolic Anderson model starting from a Dirac delta initial measure.
MSC 2010 subject classifications: Primary 60H15; Secondary 35R60, 60G60.
Keywords: stochastic heat equation, parabolic Anderson model, Malliavin calculus, negative moments, regularity of density, strict positivity of density, measure-valued initial conditions, spatially colored noise.
[CH19b] Le Chen & Jingyu Huang (2019) ‘Regularity and strict positivity of densities for the stochastic heat equation on \(\mathbb{R}^d\)’, Preprint arXiv:1902.02382
@article{chen.huang:19:regularity,
title = {Regularity and strict positivity of densities for the stochastic heat equation on $\mathbb{R}^d$},
author = {Le Chen and Jingyu Huang},
year = {2019},
month = {February},
journal = {Preprint arXiv:1902.02382},
url = {https://www.arxiv.org/abs/1902.02382}
}
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