Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4616309 | Journal of Mathematical Analysis and Applications | 2013 | 15 Pages |
Abstract
This paper is concerned with the distribution properties of the binomial aX+bXα, where X is a gamma random variable. We show in particular that aX+bXα is infinitely divisible for all αâ[1,2] and a,bâR+, and that for α=2 the second order polynomial aX+bX2 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Nicolas Privault, Dichuan Yang,