Theory of Probability &Its Applications, Volume 66, Issue 3, Page 430-444, January 2021.
For a given set of independent random variables (r.v.'s) $X_1,\dots,X_d$ belonging to a given Meixner class, we seek r.v.'s $Y_1,\dots,Y_d$ such that the marginal laws and the laws of the sums match: $Y_i\stackrel{d}{=} X_i$ and $\sum_iY_i\stackrel{d}{=}\sum_iX_i$. We give a full characterization of the r.v.'s $Y_1,\dots,Y_d$ and propose extensions and practical constructions by means of finite mean square expansions.

中文翻译：

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匹配 Meixner 类的边际分布和总和

Theory of Probability & Its Applications，第 66 卷，第 3 期，第 430-444 页，2021 年 1 月。
对于属于给定 Meixner 类的一组给定的独立随机变量 (rv's) $X_1,\dots,X_d$，我们寻求 rv's $ Y_1,\dots,Y_d$ 使得边际定律和求和定律匹配：$Y_i\stackrel{d}{=} X_i$ 和 $\sum_iY_i\stackrel{d}{=}\sum_iX_i$。我们给出了房车 $Y_1,\dots,Y_d$ 的完整特征，并通过有限均方扩展提出了扩展和实际构造。