International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 1, Pages 33-36
doi:10.1155/S0161171295000032
On complete convergence of the sum of a random number of a stable type P random elements
André Adler1
and Andrey Volodin2
1Department of Mathematics, Illinois Institute of Technology, Chicago 60616, IL, USA
2Research Institute of Mathematics, Kazan University, Tatarstan, Kazan 420008, Russia
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}.