1. Infinite divisibility of interpolated gamma powers.
- Author
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Privault, Nicolas and Yang, Dichuan
- Subjects
- *
INFINITY (Mathematics) , *DISTRIBUTION (Probability theory) , *BINOMIAL distribution , *RANDOM variables , *POLYNOMIALS , *INTEGRALS - Abstract
Abstract: This paper is concerned with the distribution properties of the binomial , where is a gamma random variable. We show in particular that is infinitely divisible for all and , and that for the second order polynomial is a generalized gamma convolution whose Thorin density and Wiener–gamma integral representation are computed explicitly. As a byproduct we deduce that fourth order multiple Wiener integrals are in general not infinitely divisible. [Copyright &y& Elsevier]
- Published
- 2013
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