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arXiv · 2007.02223

Super-convergence analysis on exponential integrator for stochastic heat equation driven by additive fractional Brownian motion

Jialin Hong·Chuying Huang
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Abstract

In this paper, we consider the strong convergence order of the exponential integrator for the stochastic heat equation driven by an additive fractional Brownian motion with Hurst parameter $H\in(\frac12,1)$. By showing the strong order one of accuracy of the exponential integrator under appropriote assumptions, we present the first super-convergence result in temporal direction on full discretizations for stochastic partial differential equations driven by infinite dimensional fractional Brownian motions with Hurst parameter $H\in(\frac12,1)$. The proof is a combination of Malliavin calculus, the $L^p(Ω)$-estimate of the Skorohod integral and the smoothing effect of the Laplacian operator.

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Jialin Hong, Chuying Huang. 2020-07-05. Super-convergence analysis on exponential integrator for stochastic heat equation driven by additive fractional Brownian motion. https://arxiv.org/abs/2007.02223

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