Conditions for the unlimited growth in multitype population size dependent Galton-Watson processes (Q749472)

The problem concerning branching processes posed by Galton and Watson was solved first by \textit{J. F. Steffensen} [see Ann. Inst. H. Poincaré 3, 319-344 (1933; Zbl 0007.02105)]. A multitype branching process is a stochastic model of the growth of a population consisting of several types of individuals who produce offspring according to stochastic laws. The author studies under what conditions a population can grow beyond any bound with positive probability. The author studies transience and recurrence of a population from the first two moments of offspring distributions. By applying \textit{G. Kersting}'s results [J. Appl. Probab. 23, 614-625 (1986; Zbl 0611.60084)] the author gives sufficient condition for transience and recurrence.