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June, 1973 On Khintchine's Estimate for Large Deviations
David G. Kostka
Ann. Probab. 1(3): 509-512 (June, 1973). DOI: 10.1214/aop/1176996946


The large deviation estimate, used in classical proofs of the law of the iterated logarithm for i.i.d. random variables, implies the random variables satisfy a condition more stringent than a finite variance. Thus it is impossible to prove the law of the iterated logarithm in its full strength (i.e. assuming only a finite second moment) by using such a deviation estimate in a "straightforward" manner.


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David G. Kostka. "On Khintchine's Estimate for Large Deviations." Ann. Probab. 1 (3) 509 - 512, June, 1973.


Published: June, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0318.60021
MathSciNet: MR356189
Digital Object Identifier: 10.1214/aop/1176996946

Primary: 60F10
Secondary: 60F05 , 60G50

Keywords: Gaussian tail estimates , large deviations , Law of the iterated logarithm

Rights: Copyright © 1973 Institute of Mathematical Statistics

Vol.1 • No. 3 • June, 1973
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