The purpose of this paper is to revisit the numerical solutions of stochastic differential equations (SDEs). An important drawback when integrating SDEs numerically is the number of steps required to attain acceptable accuracy of convergence to the true solution.,This paper develops a bias reducing method based loosely on extrapolation.,The method is seen to perform acceptably well and for realistic steps sizes provides improved accuracy at no significant additional computational cost. In addition, the optimal step size of the bias reduction methods is shown to be consistent with theoretical analysis.,Overall, there is evidence to suggest that the proposed method is a viable, easy to implement competitor for other commonly used numerical schemes.

中文翻译：

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再谈随机微分方程的数值解

本文的目的是重新讨论随机微分方程（SDE）的数值解。对SDE进行数值积分时，一个重要的缺点是要达到可接受的收敛精度才能达到真实解所需的步骤数。，本文开发了一种基于外推法的偏差减小方法。该方法被认为执行得很好并且适用于实际步骤大小提供了改进的准确性，而没有显着的额外计算成本。此外，偏差减小方法的最佳步长大小与理论分析一致。总体而言，有证据表明，该方法是其他常用数值方案的可行且易于实现的竞争对手。