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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Convergence rate for a large deviation probability


Author: David G. Kostka
Journal: Proc. Amer. Math. Soc. 43 (1974), 393-396
MSC: Primary 60F10
MathSciNet review: 0345174
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Abstract: It is known that a condition more stringent than a finite variance is needed to show, by a direct application of large deviation estimates, the convergence of the series used in classical proofs of the law of the iterated logarithm. However, the series still converges if the variables have only a finite variance.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0345174-0
PII: S 0002-9939(1974)0345174-0
Keywords: Large deviations, law of the iterated logarithm, Skorohod representation, Gaussian tail estimates, law of large numbers
Article copyright: © Copyright 1974 American Mathematical Society