Series Representation of Jointly SαS Distribution via A New Type of Symmetric Covariations

10/01/2019

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by   Yujia Ding, et al.

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We introduce a new measure of dependency between coordinates of a symmetric α-stable random vector that we call the symmetric covariation. Unlike the conventional covariation which is defined for α∈(1,2], this symmetric covariation is valid for α∈(0,2]. We show that this symmetric covariation is well-defined, using a new type of generalized fractional derivative. Properties of the symmetric covariation similar to that of the covariance functions have been derived. The main fruit of this framework is a new representation of the characteristic function of the bivariate symmetric α-stable distribution via convergent series based on these symmetric covariations.