Associated to each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided. Attention, however, is focused on applications. Indeed, such numbers describe the moments of sums of i.i.d. random variables, determining their precise asymptotic behavior without making use of the central limit theorem. Such numbers also allow us to obtain explicit and simple Edgeworth expansions. Applications to L\'{e}vy processes and cumulants are discussed, as well.

中文翻译：

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第二类概率斯特林数及其应用

与满足适当可积条件的每个复值随机变量相关联，我们引入了第二类斯特林数的不同推广。提供了各种等效定义。然而，注意力集中在应用程序上。事实上，这样的数字描述了 iid 随机变量之和的矩，在不使用中心极限定理的情况下确定了它们的精确渐近行为。这些数字还允许我们获得明确和简单的 Edgeworth 展开。还讨论了 L\'{e}vy 过程和累积量的应用。