We consider unbiased simulation methods for one-dimensional stochastic differential equations with reflection at zero. In particular, we propose improvements of the forward unbiased simulation method provided by Alfonsi et al. (Parametrix methods for one-dimensional reflected SDEs. Modern problems of stochastic analysis and statistics: selected contributions in honor of Valentin Konakov. Springer, pp 43–66, 2017). In this paper, we will apply the Poisson kernel method to improve the negativity and high variance problems of the associated simulation method. We also discuss some choices for the behavior of the approximation process near the boundary. This improvement is demonstrated through some numerical experiments.

中文翻译：

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带有反射的随机微分方程的泊松核方法的无偏模拟方法

我们考虑反射为零的一维随机微分方程的无偏模拟方法。特别是，我们提出了 Alfonsi 等人提供的前向无偏模拟方法的改进。（用于一维反射 SDE 的参数方法。随机分析和统计的现代问题：为纪念 Valentin Konakov 做出的精选贡献。Springer，第 43-66 页，2017 年）。在本文中，我们将应用泊松核方法来改善相关模拟方法的负性和高方差问题。我们还讨论了边界附近近似过程行为的一些选择。通过一些数值实验证明了这种改进。