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A note on asymptotics of linear combinations of IID random variables. (English) Zbl 1224.60033
Let X 1 ,X 2 , be i.i.d. random variables with the common distribution function F. For n=1,2,, consider the linear combination S a n =a n,1 X 1 +a n,2 X 2 ++a n,n X n , where a n =a n,1 ,a n,2 ,,a n,n is an arbitrary sequence of weights. The author investigates the asymptotic distribution of S a n under the negligibility condition. He proves that, if S a n is asymptotically normal, then the distribution F belongs to the domain of attraction of the 2-stable law.
60F05Central limit and other weak theorems
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