论文标题
统一的稳定分布方法的方法
A Unified Approach to Stein's Method for Stable Distributions
论文作者
论文摘要
在本文中，我们首先回顾Lévy过程与无限划分的随机变量之间的联系，以及无限划分的分布的分类。使用此连接和特征函数的lévy-khinchine表示，我们为无限分开的随机变量建立了Stein身份。分类和稍微修改的方法为我们提供了$α$稳定的随机变量的Stein身份，$α\ in（0,2）。$使用良好的规律性估算来解决Stein方程的解决方案，我们在$α$稳定的近似值中得出了误差范围。然后，我们应用这些结果以获得收敛速率。最后，我们将这些速率与文献中可用的结果进行了比较。
In this article, we first review the connection between Lévy processes and infinitely divisible random variables, and the classification of infinitely divisible distributions. Using this connection and the Lévy-Khinchine representation of the characteristic function, we establish a Stein identity for an infinitely divisible random variable. The classification and slight modification in approach give us a Stein identity for an $α$-stable random variable with $α\in (0,2).$ Using fine regularity estimates for the solution to Stein equation, we derive error bounds for $α$-stable approximations. We then apply these results to obtain rates of convergence. Finally, we compare these rates with the results available in the literature.
