论文标题
第二类和应用的概率stirl数字
Probabilistic Stirling numbers of the second kind and applications
论文作者
论文摘要
与满足适当的集成性条件的每个复杂价值的随机变量相关联，我们引入了第二类的stirling数字的不同概括。提供了各种等效定义。但是，注意专注于应用。实际上，这样的数字描述了I.I.D的总和的时刻。随机变量，确定其精确的渐近行为，而无需使用中央限制定理。这样的数字还使我们能够获得明确而简单的Edgeworth扩展。还讨论了对Lévy过程和累积物的申请。
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 Lévy processes and cumulants are discussed, as well.
