International Journal of Mathematics and Mathematical Sciences 
Volume 2004 (2004), Issue 19, Pages 975-990
doi:10.1155/S0161171204303194

Random sums of random vectors and multitype families of productive individuals

I. Rahimov1,2 and H. Muttlak3

 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

Abstract

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 n-type indecomposable critical branching stochastic processes with types of individuals T1,…,Tn.