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On the infinite sums of deflated Gaussian products

   
@article{ECP1921,
	author = {Enkelejd Hashorva and Lanpeng Ji and Zhongquan Tan},
	title = {On the infinite sums of deflated Gaussian products},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {17},
	year = {2012},
	keywords = {Gaussian products; infinite sums; random deflation; exact tail asymptotics; max-domain of attraction; regular variation; chi-square distribution},
	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.
},
	pages = {no. 31, 1-8},
	issn = {1083-589X},
	doi = {10.1214/ECP.v17-1921},    
        url = {http://ecp.ejpecp.org/article/view/1921}}