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Teoriya Veroyatnostei i ee Primeneniya, 1977, Volume 22, Issue 1, Pages 18–26
(Mi tvp3099)
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This article is cited in 16 scientific papers (total in 16 papers)
On necessary and sufficient conditions for the law of the iterated logarithm
A. I. Martikaĭnen, V. V. Petrov Leningrad State University
Abstract:
Let $\{X_n;\,n=1,2,\dots\}$ be a sequence of independent not necessarily identically distributed random variables and $\{a_n;\,n=1,2,\dots\}$ be a non-decreasing sequence of positive numbers such that $a_n\to\infty$. We put $\displaystyle S_n=\sum_{j=1}^n X_j$. Necessary and sufficient conditions are found for the relations $\limsup(S_n/a_n)\le 1$ a.s. and $\limsup(S_n/a_n)=1$ a.s. No assumptions about existence of any moments are made.
Received: 16.12.1975
Citation:
A. I. Martikaǐnen, V. V. Petrov, “On necessary and sufficient conditions for the law of the iterated logarithm”, Teor. Veroyatnost. i Primenen., 22:1 (1977), 18–26; Theory Probab. Appl., 22:1 (1977), 16–23
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