On complete convergence of the sum of a random number of a stable type P random elements
André Adler1and Andrey Volodin2
Received01 Sept 1992
Revised10 Mar 1993
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}.