论文标题
对随机热方程的指数积分器的超级通用分析，由加性分数布朗运动驱动
Super-convergence analysis on exponential integrator for stochastic heat equation driven by additive fractional Brownian motion
论文作者
论文摘要
在本文中，我们考虑了由添加剂分数布朗运动驱动的随机热方程的指数积分器的强收敛顺序，并以Hurst参数$ h \ in（\ frac12,1）$。通过显示适当假设下指数积分器的准确性之一，我们介绍了第一个超级连接导致的时间方向在完全离散的时间方向上，用于完全离散的随机部分差分方程，该方程由无限分数布朗尼运动带有hurst参数$ h \ in（\ frac12,12,1,1）$。证明是Malliavin微积分的组合，$ l^p（ω）$ - Skorohod积分的估计值和Laplacian操作员的平滑效果。
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.
