On the infinite divisibility of the product of two г-distributed stochastical variables

摘要

The authors give a positive answer to the question “if Xα is г-distributed of order α, and Xβ of order β, with Xα and Xβ independent, is XαXβ infinitely divisible?”. This question, posed by Steutel in Ref. 1, has not been answered up to now, so far as they can find in the literature. In addition they show that the distribution of XαXβ is a generalized г-distribution.