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Cramér theorem for Gamma random variables


 
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1. Title Title of document Cramér theorem for Gamma random variables
 
2. Creator Author's name, affiliation, country Solesne Bourguin; Université Paris 1
 
2. Creator Author's name, affiliation, country Ciprian A. Tudor; Université Lille 1
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Cramér's theorem, Gamma distribution, multiple stochastic integrals, limit theorems, Malliavin calculus
 
3. Subject Subject classification 60F05; 60H05; 91G70
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ANR
 
7. Date (YYYY-MM-DD) 2011-07-07
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1639
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1639
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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