Geometric growth in near-supercritical population size dependent multitype Galton-Watson processes
A population process with finitely many types is considered in which the branching property holds except that the offspring distributions depend upon the current population size. It is shown that if the mean matrix of offspring distributions converges, as the population size becomes large, to that of a supercritical branching process, then the asymptotic growth of the process essentially mimics that of the ``limit'' branching process in its geometric growth. For mean square normed convergence, conditions on the variances are required. Some sufficient conditions for geometric growth are also stated and proved. The paper generalizes results for one-type processes given by the author [J. Appl. Probab. 21, 40-49 (1984; Zbl 0544.60073)].
scientific article; zbMATH DE number 4137149