Convolution Equivalence and Infinite Divisibility: Corrections and Corollaries

On infinite divisibility and embedding of probability measures on a locally compact Abelian group

In the present note the authors supplement significant properties of infinitely divisible and embeddable probability measures on a locally compact Abelian group G. There are at least two versions of infinite divisibility appearing in the literature which deserve special attention, and the problem of embedding those measures leads directly to the study of continuous convolution semigroups on G. ...

Infinitely Divisible Distributions for Rectangular Free Convolution: Classification and Matricial Interpretation

In a previous paper ([B-G1]), we defined the rectangular free convolution ⊞ λ . Here, we investigate the related notion of infinite divisibility, which happens to be closely related the classical infinite divisibility: there exists a bijection between the set of classical symmetric infinitely divisible distributions and the set of ⊞ λ -infinitely divisible distributions, which preserves limit t...

Lévy processes on a first order model

The classical notion of a Lévy process is generalized to one that takes values in an arbitrary model of a first order language. This is achieved by defining a convolution product and the infinite divisibility with respect to it.

Additions and Corrections "M.H.Alamatsaz- On Modality and Divisibility of Poisson and Binomial Mixtures. J.Sci. I.R. Iran, Vol.l,No.3, Spring 1990

Infinite divisibility of interpolated gamma powers

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 α ∈ [1, 2] and a, b ∈ R+, 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....