@article{EJP961,
author = {Theofanis Sapatinas and Damodar Shanbhag and Arjun Gupta},
title = {Some New Approaches to Infinite Divisibility},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {16},
year = {2011},
keywords = {Kaluza sequences; Infinite divisibility; Log-convexity; Mixtures of exponential distributions; Mixtures of geometric distributions; Wiener-Hopf factorization},
abstract = {Using an approach based, amongst other things, on Proposition 1 of Kaluza (1928), Goldie (1967) and, using a different approach based especially on zeros of polynomials, Steutel (1967) have proved that each nondegenerate distribution function (d.f.) $F$ (on $\mathbb{R}$, the real line), satisfying $F(0-)=0$ and $F(x)=F(0)+(1-F(0))G(x), x > 0$, where $G$ is the d.f. corresponding to a mixture of exponential distributions, is infinitely divisible. Indeed, Proposition 1 of Kaluza (1928) implies that any nondegenerate discrete probability distribution $\{p_x:x=0,1,\ldots\}$ that is log-convex or, in particular, completely monotone, is compound geometric, and, hence, infinitely divisible. Steutel (1970), Shanbhag & Sreehari (1977) and Steutel & van Harn (2004, Chapter VI) have given certain extensions or variations of one or more of these results. Following a modified version of the C.R. Rao et al. (2009, Section 4) approach based on the Wiener-Hopf factorization, we establish some further results of significance to the literature on infinite divisibility.},
pages = {no. 85, 2359-2374},
issn = {1083-6489},
doi = {10.1214/EJP.v16-961},
url = {http://ejp.ejpecp.org/article/view/961}}