Mathematical Problems in Engineering
Volume 7 (2001), Issue 1, Pages 87-95

The strong law of large numbers for dependent vector processes with decreasing correlation: “Double averaging concept”

Alex S. Poznyak

CINVESTAV-IPN, Department of Automatic Control, A. P. 14-740, Mexico D.F. CP-07300, Mexico

Received 10 October 2000

Copyright © 2001 Alex S. Poznyak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new form of the strong law of large numbers for dependent vector sequences using the “double averaged” correlation function is presented. The suggested theorem generalizes the well-known Cramer–Lidbetter's theorem and states more general conditions for fulfilling the strong law of large numbers within the class of vector random processes generated by a non stationary stable forming filters with an absolutely integrable impulse function.