We consider a kind of Collision Branching Processes with Immigration (CBIP). Some important properties of the generating functions for the CBI q-matrix were first investigated in detail. Then for any given CBI q-matrix, the existence and uniqueness of CBIP is proved, and sufficient and easily...

This note provides a new probabilistic approach in discussing the weighted Markov branching process (WMBP) which is a natural generalisation of the ordinary Markov branching process. Using this approach, some important characteristics regarding the hitting times of such processes can be easily...

We extend the Harris regularity condition for ordinary Markov branching process to a more general case of non-linear Markov branching process. A regularity criterion which is very easy to check is obtained. In particular, we prove that a super-linear Markov branching process is regular if and...