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