论文标题
斯坦因恢复稳定分布的方法
Stein's Method for Tempered Stable Distributions
论文作者
论文摘要
在本文中，我们开发了双面钢化稳定分布的Stein表征。文献中已经知道的正常，伽马，拉普拉斯和方差γ分布的Stein表征很容易遵循。一个人还可以为更困难的分布（例如两个正常随机变量的产物分布，两个伽玛随机变量之间的差异。使用Semigroup方法，我们获得了Stein方程解决方案的估计值。最后，我们应用这些估计值在三个知名问题中以恢复稳定的近似值来获得误差范围：在两个稳定稳定分布，随机几何总和的拉普拉斯近似值和六矩定理之间的比较中，对符号级别差异近似niener-it $ $ $ $ \ dddot的函数近似值的对称性差异近似。我们还将结果与现有文献进行了比较。
In this article, we develop Stein characterization for two-sided tempered stable distribution. Stein characterizations for normal, gamma, Laplace, and variance-gamma distributions already known in the literature follow easily. One can also derive Stein characterizations for more difficult distributions such as the distribution of product of two normal random variables, a difference between two gamma random variables. Using the semigroup approach, we obtain estimates of the solution to Stein equation. Finally, we apply these estimates to obtain error bounds in the Wasserstein-type distance for tempered stable approximation in three well-known problems: comparison between two tempered stable distributions, Laplace approximation of random geometric sums, and six moment theorem for the symmetric variance-gamma approximation of functionals of double Wiener-It$\ddot{\text{o}}$ integrals. We also compare our results with the existing literature.
