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 $L^p(\Omega)$-estimate of the Skorohod integral and the smoothing effect of the Laplacian operator.

中文翻译：

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加性分数布朗运动驱动的随机热方程指数积分器的超收敛分析

在本文中，我们考虑了由具有 Hurst 参数 $H\in(\frac12,1)$ 的加性分数布朗运动驱动的随机热方程的指数积分器的强收敛阶数。通过在适当的假设下显示指数积分器精度的强阶一，我们提出了由具有 Hurst 参数的无限维分数布朗运动驱动的随机偏微分方程完全离散化在时间方向上的第一个超收敛结果\frac12,1)$。证明是 Malliavin 微积分、Skorohod 积分的 $L^p(\Omega)$ 估计值和拉普拉斯算子的平滑效果的组合。