Study of the limiting behavior of delayed random sums under non-identical distributions setup and a Chover type LIL

Abstract

We consider delayed sums of the type Sn+an − Sn where an is possibly a positive integer valued random variable satisfying certain conditions and Sn is the sum of independent random variables Xn with distribution functions Fn ∈ {G1, G2}. We study the limiting behavior of the delayed sums and prove laws of the iterated logarithm of Chover type. These results extend the results in Vasudeva and Divanji (1992) and Chen (2008).