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 | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1974-0345174-0

Keywords:
Large deviations,
law of the iterated logarithm,
Skorohod representation,
Gaussian tail estimates,
law of large numbers

Article copyright:
© Copyright 1974
American Mathematical Society