branching migration stopped at zero life-period extinction moments limit theorems Department of Probability and Statistics
Institute of Mathematics with Computer Center at the Bulgarian Academy of Sciences
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.