Asymptotic properties of multitype critical branching processes evolving in a random environment

摘要

For an extended class of multitype critical branching processes in a random environment, the asymptotic behaviour of the survival probability is found under the conditions which are weaker than those known earlier even for the single-type case. A functional limit theorem is proved for the number of particles in the process at moments nt , 0 ≤ t≤ 1, conditioned on its survival up to moment n. This research was supported by the Russian Foundation for Basic Research (grant 08– 01–00078) and by the Programme of Russian Academy of Sciences ‘Mathematical Theory of Control.’