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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Sums of stationary sequences cannot grow slower than linearly


Author: Harry Kesten
Journal: Proc. Amer. Math. Soc. 49 (1975), 205-211
MSC: Primary 60F15; Secondary 28A65
DOI: https://doi.org/10.1090/S0002-9939-1975-0370713-4
MathSciNet review: 0370713
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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that for a stationary sequence of random variables $ {X_1},{X_2}, \cdots $ one has

$\displaystyle \lim \inf {n^{ - 1}}\sum\limits_{i = 1}^n {{X_i} > 0} $

a.e. on the set $ \{ \Sigma _1^n{X_i} \to \infty ,n \to \infty \} $.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0370713-4
Keywords: Stationary sequences, ergodic theorem, rate of convergence to infinity of partial sums
Article copyright: © Copyright 1975 American Mathematical Society