On the infinite sums of deflated Gaussian products

Enkelejd Hashorva (University of Lausanne)
Lanpeng Ji (University of Lausanne)
Zhongquan Tan (Jiaxing University)

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.


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Pages: 1-8

Publication Date: July 23, 2012

DOI: 10.1214/ECP.v17-1921

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