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Shanbhag, Theofanis Sapatinas","submitted_at":"2009-09-29T08:32:06Z","abstract_excerpt":"Ramachandran (1969, 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 L$\\acute{\\rm e}$vy measure. A generalized version of this result in the case of multivariate infinitely divisible distributions, involving the concept of g-moments, is given by Sato (1999, Theorem 25.3). 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