Document Type

Article

Publication Date

2-26-2019

Publication Title

Annals of Probability

Volume

47

Issue

2

First page number:

989

Last page number:

1035

Abstract

We establish the strong comparison principle and strict positivity of solutions to the following nonlinear stochastic heat equation on Rd (∂∂t−12Δ)u(t,x)=ρ(u(t,x))M˙(t,x), for measure-valued initial data, where M˙ is a spatially homogeneous Gaussian noise that is white in time and ρ is Lipschitz continuous. ... (See full text for complete abstract)

Keywords

Stochastic heat equation; Parabolic Anderson model; Space-time Hölder regularity; Spatially homogeneous noise; Comparison principle; Measure-valued initial data

Disciplines

Applied Mathematics

File Format

pdf

File Size

382 KB

Language

English

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