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2011 Cramér theorem for Gamma random variables
Solesne Bourguin, Ciprian Tudor
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Electron. Commun. Probab. 16: 365-378 (2011). DOI: 10.1214/ECP.v16-1639

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.

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Solesne Bourguin. Ciprian Tudor. "Cramér theorem for Gamma random variables." Electron. Commun. Probab. 16 365 - 378, 2011. https://doi.org/10.1214/ECP.v16-1639

Information

Accepted: 7 July 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1272.68116
MathSciNet: MR2819659
Digital Object Identifier: 10.1214/ECP.v16-1639

Subjects:
Primary: 60F05
Secondary: 60H05, 91G70

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