Abstract We propose a local linearization scheme to approximate the solutions of non-autonomous stochastic differential equations driven by fractional Brownian motion with Hurst parameter Toward this end, we approximate the drift and diffusion terms by means of a first-order Taylor expansion. This becomes the original equation into a local fractional linear stochastic differential equation, whose solution can be figured out explicitly. As in the Brownian motion case (i.e., H = 1/2), the rate of convergence, in our case, is twice the one of the Euler scheme. Numerical examples are given to demonstrate the performance of the method.

中文翻译：

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分数布朗运动驱动的随机微分方程的局部线性化方法

摘要 我们提出了一种局部线性化方案来逼近由具有 Hurst 参数的分数布朗运动驱动的非自治随机微分方程的解。为此，我们通过一阶泰勒展开来逼近漂移和扩散项。这将原始方程变为局部分数阶线性随机微分方程，其解可显式计算。在布朗运动的情况下（即，H = 1/2），在我们的情况下，收敛速度是欧拉方案的两倍。给出了数值例子来证明该方法的性能。