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June, 1974 Limit Theorems for Delayed Sums
Tze Leung Lai
Ann. Probab. 2(3): 432-440 (June, 1974). DOI: 10.1214/aop/1176996658


In this paper, we study analogues of the law of the iterated logarithm for delayed sums of independent random variables. In the i.i.d. case, necessary and sufficient conditions for such analogues are obtained. We apply our results to find convergence rates for expressions of the form $P\lbrack |S_n| > b_n \rbrack$ and $P\lbrack \sup_{k\geqq n} |S_k/b_k| > \varepsilon \rbrack$ for certain upper-class sequences $(b_n)$. In this connection, certain theorems of Erdos, Baum and Katz are also generalized.


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Tze Leung Lai. "Limit Theorems for Delayed Sums." Ann. Probab. 2 (3) 432 - 440, June, 1974.


Published: June, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0305.60009
MathSciNet: MR356193
Digital Object Identifier: 10.1214/aop/1176996658

Keywords: 6030 , Delayed first arithmetic means , Kolmogrovov's exponential bounds , law of the the iterated logarithm , rate of convergence , upper-class sequences

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 3 • June, 1974
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