TRANSIENCE AND RECURRENCE OF BRANCHING PROCESSES WITH STATE-DEPENDENT OFFSPRING DISTRIBUTIONS

摘要

Let (X sub n) denote the Galton-Watson branching process with immigration at the zero state, and reproduction via the i'th of a countable set of offspring distributions, when (X sub n) = i not = 0. Conditions are presented which are sufficient for transience, recurrence, and positive-recurrence of (X sub n).