On Critical Branching Migration Processes with Predominating Emigration

The branching migration processes generalize the classical Bienaymé - Watson process allowing a migration component in each generation: with probability p the offspring of one particle is eliminated (family emigration) or with probability q there is not any migration or with probability r a state-dependent immigration of new particles is available, p + q + r = 1. The processes stopped at zero are also considered. It is investigated the critical case when the migration mean in the non-zero states is negative (predominating emigration). The asymptotic behaviour of the life-period, the probability of non-extinction and moments is obtained and limit theorems are also proved

Limit Theorems for Age-Dependent Branching Processes with State-Dependent Immigration

[Slavtchova-Bojkova Maroussia N.; Славчова-Божкова Маруся Н.]; [Yanev Nickolay M.; Янев Николай М.]We consider a model of Bellman-Harris branching processes with immigration only in the state zero (BHIO) which permits in addition an immigration component of i.i.d. BHIO processes entering the population at i.i.d. times of an independent renewal process (BHIOR). Asymptotic properties and limit theorems are proved in поп-critical cases. 60J8

Analysis of a recurrence related to critical non-homogeneous Branching processes

Some classes of controlled branching processes (with nonhomogeneous migration or with nonhomogeneous state-dependent immigration) lead in the critical case to a recurrence for the extinction probabilities. Under some additional conditions it is known that this recurrence depends on some parameter β and converges for 0 < β < 1. Now we show that the recurrence does converge for all positive values of the parameter β, which leads to an extension of some limit theorems for the corresponding branching processes. We also give a generalization of the recurrence and an asymptotic analysis of its behavior.SCOPUS: ar.jinfo:eu-repo/semantics/publishe