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In this paper we derive the exact tail asymptotic behaviour of S∞=∑∞ i= 1λ iX iY i, where λ i, i ≥ 1, are non-negative square summable deflators (weights) and X i, Y i, i ≥ 1, are independent standard Gaussian random variables. Further, we consider the tail asymptotics of S∞;p=∑∞ i=1λ iX i|Y i|p, p > 1, and also discuss the influence on the asymptotic results when λ i's are independent random variables.

On the infinite sums of deflated Gaussian products