Convergence of Density Approximations for Stochastic Heat Equation

Chuchu Chen; Jianbo Cui; Jialin Hong; Derui Sheng

doi:10.1093/imanum/drac011

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arXiv · 2007.12960

Convergence of Density Approximations for Stochastic Heat Equation

Chuchu Chen·Jianbo Cui·Jialin Hong·Derui Sheng

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Abstract

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.

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Chuchu Chen, Jianbo Cui, Jialin Hong, Derui Sheng. 2020-07-25. Convergence of Density Approximations for Stochastic Heat Equation. https://doi.org/10.1093/imanum%2Fdrac011

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