Abstract

A new class of branching processes allowing a random migration component in every generation is considered: with probability p two types of emigration are possible — a random number of families and a random number of individuals, or with probability q there is not any migration (i.e. the process develops like a Bienaymé-Galton-Watson process), or with probability r a state-dependent immigration of new individuals is available, p + q + r = 1. The coresponding processes stopped at zero are studied in the critical case and the asymptotic behaviour of the non-extinction probability is obtained (depending on the range of an extra critical parameter).branching processrandom migrationextinction 60J80

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