On complete convergence of the sum of a random number of a stable type P random elements

Abstract

Complete convergence for randomly indexed normalized sums of random elements of the form ∑j=1TnXj/ϕ(Tn) is established. The random elements {Xn} belong to a type p stable space and are assumed to be independent, but not necessarily identically distributed. No assumptions are placed on the joint distributions of the stopping times {Tn}.