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
File Size
382 KB
Language
English
Repository Citation
Chen, L.,
Huang, J.
(2019).
Comparison Principle for Stochastic Heat Equation on Rd.
Annals of Probability, 47(2),
989-1035.
http://dx.doi.org/10.1214/18-AOP1277
