Growth of Sums of Pairwise Independent Random Variables with Infinite Expectations

摘要

It is proved that P{|Sn| > an infinitely often}=0 or 1 if the series ∑_n=1~∞ P{|Xn| > an is convergent or nonconvergent, where S_n=X_1+…+X_n is a sum of identically distributed pairwise independent random variables with infinite expectations, a_n > 0, for some m a sequence {an} n≥m strictly increasing and convex.