A GENERALIZATION OF THE HSU-ROBBINS-ERDOS THEOREM

[摘要] In case (X(n)) is an i.i.d. sequence, and S(n) = X(l) + ... + X(n), the Hsu-Robbins-Erdos theorem states that SIGMA(n=1)xP(\S(n)\>nepsilon) < infinity, epsilon > 0, iff EX1(2) < infinity and EX1 = 0. The purpose of this paper is to generalize this result to the case in which the steps X(n) are independent, but their distributions are taken from a finite set. (C) 1994 Academic Press, Inc.

[发布日期] 1994-10-15