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A Condition For Existence Of Moments Of Infinitely Divisible Distributions

Published online by Cambridge University Press:  20 November 2018

J. M. Shapiro
J. M. Shapiro*
Affiliation:
Ohio State University
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Let F(x) be an infinitely divisible distribution and let ϕ(t) be its characteristic function. As is well known according to the formula of Lévy and Khintchine, ϕ(t) has the following representation:

1

where γ is a real constant and G(u) is a bounded nondecreasing function.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 69 - 71
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Cramér, Harald, Mathematical methods of statistics (Princeton University Press, 1946).Google Scholar