Journal of the
Korean Mathematical Society JKMS

In this paper we consider an age dependent branching process whose particles move according to a Markov process with continuous state space. The Markov process is assumed to be stationary with independent increments and positive recurrent. We find some sufficient conditions for the Markov motion process such that the empirical distribution of the positions converges to the limiting distribution of the motion process.

Keywords: age-dependent branching process, law of large numbers, point measure process, positive recurrent Markov process

MSC numbers: 60J80, 60J30