International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 19, Pages 975-990
Random sums of random vectors and multitype families of
1Institute of Mathematics, Uzbek Academy of Sciences, Tashkent 700143, Uzbekistan
2Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, P.O. Box 1339, Dhahran 31261, Saudi Arabia
3Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, P.O. Box 1676, Dhahran 31261, Saudi Arabia
Received 25 March 2003
Copyright © 2004 I. Rahimov and H. Muttlak. 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.
We prove limit theorems for a family of random vectors whose
coordinates are a special form of random sums of
Bernoulli random variables. Applying these limit theorems, we
study the number of productive individuals in -type
indecomposable critical branching stochastic processes with types
of individuals .