On scaling limits of age dependent branching processes with Markovian motion

Abstract: Consider an age dependent branching processes where individuals execute independent copies of a Markov process in R during their lifetime starting from where their parent dies. At time t consider the age and spatial distribution of the individuals.The following results will be established.

1. For a randomly chosen individual at time t the joint distribution of the age unscaled and position scaled by root t will be shown to converge to independent rv.

2. The empirical distribution of the age unscaled and position scaled by root t will be shown to converge to random one in the critical case and a deterministic one in the supercritical case.

3. A super-process limit (ie a measure valued process) will be established for a sequence of populations with increasing initial population and time suitably scaled.