Supercritical age-dependent branching Markov processes and their scaling limits

Abstract

This paper studies the long-time behavior of the empirical distribution of age and normalized position of an age-dependent supercritical branching Markov process. The motion of each individual during its life is a random function of its age. It is shown that the empirical distribution of the age and the normalized position of all individuals alive at time $t$ converges as $t→∞$ to a deterministic product measure.