Convergence of Density Approximations for Stochastic Heat Equation

This paper investigates the convergence of density approximations for stochastic heat equation in both uniform convergence topology and total variation distance. The convergence order of the densities in uniform convergence topology is shown to be exactly \(1/2\) in the nonlinear case and nearly \(1...

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Bibliographic Details
Published inarXiv.org
Main Authors Chen, Chuchu, Cui, Jianbo, Hong, Jialin, Sheng, Derui
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 03.08.2020
Subjects
Computer Science - Numerical Analysis
Convergence
Density
Mathematics - Numerical Analysis
Mathematics - Probability
Partial differential equations
Thermodynamics
Topology
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Summary:This paper investigates the convergence of density approximations for stochastic heat equation in both uniform convergence topology and total variation distance. The convergence order of the densities in uniform convergence topology is shown to be exactly \(1/2\) in the nonlinear case and nearly \(1\) in the linear case. This result implies that the distributions of the approximations always converge to the distribution of the origin equation in total variation distance. As far as we know, this is the first result on the convergence of density approximations to the stochastic partial differential equation.
ISSN:2331-8422
DOI:10.48550/arxiv.2007.12960