Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 1 , pp. 164--173

A NOTE ON THE "FAIR" GAMES PROBLEM

By

ANDRÉ ADLER, Illinois Institute of Technology

SUMMARY. Consider i.i.d. random variables {X, Xn, n 1} with either EX = 0 or E |X | = . We construct sequences {an, n 1} and {bn, n 1} so that $\sum^{n}_{k=1}a_k X_k/b_n \rightarrow 1$ a.s. Furthermore, it is shown that the conditions assumed are necessary and sufficient when selecting weights { an, n 1} and norms { bn, n 1} according to our procedure.

AMS (1980) subject classification. Primary 60F15.

Key words and phrases. Almost sure convergence, strong law of large numbers, ''fair'' games problem, slow variation.

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