We are interested in finding an approximation for the solution of stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm) with Hurst parameter $H>\frac{1}{2}$. Based on Taylor expansion we derive a numerical scheme and investigate its convergence. Under some assumptions on drift and diffusion, we show that the introduced method is convergent with strong rate of convergence ${\mathrm{\Delta }}^H$, where Δ is the diameter of partition used for discretization. In addition, we explain the simulation of the proposed method and show the accuracy of our results by presenting an example.

中文翻译：

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具有分数布朗运动的随机微分方程的数值格式的收敛性

我们感兴趣的是寻找由分数布朗运动（fBm）和Hurst参数驱动的随机微分方程（SDE）解的近似值 $H>\frac{\mathrm{1个}}{\mathrm{2个}}$。基于泰勒展开，我们导出了一个数值方案，并研究了其收敛性。在一些关于漂移和扩散的假设下，我们证明了所引入的方法具有很强的收敛速度。${\mathrm{\Delta }}^H$，其中Δ是用于离散化的分区的直径。此外，我们通过实例说明了该方法的仿真并显示了结果的准确性。