A remark on almost sure convergence of weighted sums. (English) Zbl 0599.60031

As a generalization of a theorem of Y. S. Chow [Ann. Math. Stat. 37, 1482-1493 (1966; Zbl 0152.169)] it is shown by an elementary method that for i.i.d. r.v.’s \(X_ 1,...,X_ n\), with expectation zero and finite p-th absolute moment (p\(\geq 2)\) the weighted sums \[ \sum^{n}_{i=1}a_{n,i}X_ i/n^{1/p}(\sum^{n}_{i=1}a^ 2_{n,i})^{1/2} \] converge to zero a.s.


60F15 Strong limit theorems
60G42 Martingales with discrete parameter


Zbl 0152.169
Full Text: DOI


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