@article{ECP1639,
author = {Solesne Bourguin and Ciprian Tudor},
title = {Cramér theorem for Gamma random variables},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {16},
year = {2011},
keywords = {Cramér's theorem, Gamma distribution, multiple stochastic integrals, limit theorems, Malliavin calculus},
abstract = {In this paper we discuss the following problem: given a random variable $Z=X+Y$ with Gamma law such that $X$ and $Y$ are independent, we want to understand if then $X$ and $Y$ each follow a Gamma law. This is related to Cramer's theorem which states that if $X$ and $Y$ are independent then $Z=X+Y$ follows a Gaussian law if and only if $X$ and $Y$ follow a Gaussian law. We prove that Cramer's theorem is true in the Gamma context for random variables living in a Wiener chaos of fixed order but the result is not true in general. We also give an asymptotic variant of our result.},
pages = {no. 34, 365-378},
issn = {1083-589X},
doi = {10.1214/ECP.v16-1639},
url = {http://ecp.ejpecp.org/article/view/1639}}