Moment properties of multivariate infinitely divisible laws and criteria for multivariate self-decomposability

Theofanis Sapatinas and Damodar N. Shanbhag

Journal of Multivariate Analysis, 2010, vol. 101, issue 3, 500-511

Abstract: Ramachandran (1969) [9, Theorem 8] has shown that for any univariate infinitely divisible distribution and any positive real number [alpha], an absolute moment of order [alpha] relative to the distribution exists (as a finite number) if and only if this is so for a certain truncated version of the corresponding Lévy measure. A generalized version of this result in the case of multivariate infinitely divisible distributions, involving the concept of g-moments, was given by Sato (1999) [6, Theorem 25.3]. We extend Ramachandran's theorem to the multivariate case, keeping in mind the immediate requirements under appropriate assumptions of cumulant studies of the distributions referred to; the format of Sato's theorem just referred to obviously varies from ours and seems to have a different agenda. Also, appealing to a further criterion based on the Lévy measure, we identify in a certain class of multivariate infinitely divisible distributions the distributions that are self-decomposable; this throws new light on structural aspects of certain multivariate distributions such as the multivariate generalized hyperbolic distributions studied by Barndorff-Nielsen (1977) [12] and others. Various points relevant to the study are also addressed through specific examples.

Keywords: Multivariate; generalized; hyperbolic; distributions; Multivariate; indecomposability; Multivariate; infinite; divisibility; Multivariate; self-decomposability; Stable; distributions (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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