Abstract
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>12. 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 ΔH, 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.
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