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2012 On the infinite sums of deflated Gaussian products
Enkelejd Hashorva, Lanpeng Ji, Zhongquan Tan
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Electron. Commun. Probab. 17: 1-8 (2012). DOI: 10.1214/ECP.v17-1921

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.

Citation

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Enkelejd Hashorva. Lanpeng Ji. Zhongquan Tan. "On the infinite sums of deflated Gaussian products." Electron. Commun. Probab. 17 1 - 8, 2012. https://doi.org/10.1214/ECP.v17-1921

Information

Accepted: 23 July 2012; Published: 2012
First available in Project Euclid: 7 June 2016

zbMATH: 1266.60069
MathSciNet: MR2955496
Digital Object Identifier: 10.1214/ECP.v17-1921

Subjects:
Primary: 60G70
Secondary: 60G15

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