Almost sure stability of partial sums of uniformly bounded random variables

Author:
Theodore P. Hill

Journal:
Proc. Amer. Math. Soc. **89** (1983), 685-690

MSC:
Primary 60F15; Secondary 60G42

MathSciNet review:
718997

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Abstract: Suppose , is a sequence of real numbers with . If a.s. for every sequence of independent nonnegative uniformly bounded random variables , satisfying some hypothesis condition A, then for every (arbitrarily-dependent) sequence of nonnegative uniformly bounded random variables , , a.s. on the set where the conditional distributions (given the past) satisfy precisely the same condition A. If, in addition, , then the assumption of nonnegativity may be dropped.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1983-0718997-9

Keywords:
Almost-sure stability of partial sums,
martingale strong law of large numbers,
conditional generalizations of strong laws

Article copyright:
© Copyright 1983
American Mathematical Society