Branching processes with decreasing immigration and tribal emigration (Q5930101)

Branching processes with decreasing immigration and tribal migrations are studied. A tribe of individuals enter a region according to a Poisson process and remain there for a random time interval. During this interval, they evolve according to a continuous time Markov branching process. They then emigrate from the region collectively. Formulas for the probability that the region contains at least one individual are obtained for the case of time dependent immigration. Among other things, limit distributions for the size of the population are also obtained.