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On Chover’s LIL for the weighted sums of stable random variables. (English) Zbl 1023.60038
Summary: Let \(\{X_n,n\geq 1\}\) be a sequence of \(\alpha\)-stable random variables \((0<\alpha <2)\), \(\{a_{ni},1\leq i\leq n,n\geq 1\}\) be an array of constant real numbers. Under some restriction on \(\{a_{ni},1\leq i\leq n,n\geq 1\} \), the authors discuss the integral test for the weighted partial sums \(\{ \sum^n_{i=1}a_{ni} X_i,n\geq 1\}\), and obtain Chover’s laws of the iterated logarithm as corollaries.

MSC:
60F15 Strong limit theorems
60E07 Infinitely divisible distributions; stable distributions
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