A remark on almost sure convergence of weighted sums期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A remark on almost sure convergence of weighted sums

Authors:	Rolf Thrum

Affiliation:	(1) Department of Statistics, Humboldt-University at Berlin, Unter den Linden 6, DDR-1086 Berlin, German Democratic Republic

Abstract:	Summary As a generalization of a theorem of Chow [1] it is shown by an elementary method that for i.i.d. r.v.'s X₁,...,X_n, with expectation zero and finite p-th absolute moment (p2) the weighted sums $sumlimits_{i = 1}^n {a_{n,i} X_i /n^{1/p} (sumlimits_{i = 1}^n {a_{n,i}^2 } } )^{1/2}$ converge to zero a.s.

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