Series Representation of Jointly S˛S Distribution via Symmetric Covariations

作     者：Yujia Ding Qidi Peng 

作者机构：Institute of Mathematical SciencesClaremont Graduate University1237 N.Dartmouth Ave.ClaremontCA 91711USA 

出 版 物：《Communications in Mathematics and Statistics》 (数学与统计通讯（英文）)

年 卷 期：2021年第9卷第2期

页      面：203-238页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Symmetricα-stable random vector Symmetric covariation Generalized fractional derivative Series representation 

摘      要：We introduce the notion of symmetric covariation,which is a new measure of dependence between two components of a symmetricα-stable random vector,where the stability parameterαmeasures the heavy-tailedness of its *** covariation that exists only whenα∈(1,2],symmetric covariation is well defined for allα∈(0,2].We show that symmetric covariation can be defined using the proposed generalized fractional derivative,which has broader usages than those involved in this *** properties of symmetric covariation have been *** are either similar to or more general than those of the covariance functions in the Gaussian *** main contribution of this framework is the representation of the characteristic function of bivariate symmetricα-stable distribution via convergent series based on a sequence of symmetric *** series representation extends the one of bivariate Gaussian.