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On the infinite sums of deflated Gaussian products


 
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1. Title Title of document On the infinite sums of deflated Gaussian products
 
2. Creator Author's name, affiliation, country Enkelejd Hashorva; University of Lausanne; Switzerland
 
2. Creator Author's name, affiliation, country Lanpeng Ji; University of Lausanne; Switzerland
 
2. Creator Author's name, affiliation, country Zhongquan Tan; Jiaxing University; China
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Gaussian products; infinite sums; random deflation; exact tail asymptotics; max-domain of attraction; regular variation; chi-square distribution
 
3. Subject Subject classification 60G70; 60G15
 
4. Description Abstract

In this paper we derive the exact tail asymptotic behaviour of $S_\infty=\sum_{i=1}^\infty \lambda_i X_iY_i$, where $\lambda_i, i\ge 1,$ are non-negative square summable deflators (weights) and $X_i,Y_i, i\ge1,$ are independent standard Gaussian random variables. Further, we consider the tail asymptotics of $S_{\infty;p}=\sum_{i=1}^\infty\lambda_i X_i|Y_i|^p, p> 1$, and also discuss the influence on the asymptotic results when $\lambda_i$'s are independent random variables.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Swiss National Science Foundation
 
7. Date (YYYY-MM-DD) 2012-07-23
 
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/1921
 
10. Identifier Digital Object Identifier 10.1214/ECP.v17-1921
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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