On the number of productive individuals in the Bienayme-Galton-Watson process with immigration
Let Z(tau, t) is the number of individuals at time tau having more than theta(t - tau) descendants at time t, t > tau. Here theta(t) is some non-negative function. Limit distributions for Z(tau, t) when population evolves according to critical branching processes with time homogeneous immigration and distribution of the number of descendants has finite variance are obtained. An application to study of the number of "big" trees in a forest containing a random number of trees is also discussed. (C) 2007 IMAC. Published by Elsevier B.V. All rights reserved.
finite variance reduced process gamma distribution normal distribution large population