Kevei Péter (SZTE): Subcritical Galton-Watson branching processes with immigration in random environment and random fixed point equations

SZTE, TTIK, Bolyai Intézet,  Sztochasztika szeminárium

Abstract. We investigate the tail behavior of the stationary distribution of subcritical Galton-Watson branching processes with immigration in random environment. We show that, contrary to the deterministic environment setup, the stationary distribution has typically Pareto-like tail, even with light-tailed immigration and offspring distribution. Since the stationary distribution is a solution to a random fixed point equation, Goldie's implicit renewal theory can be applied.