Although simple branching processes play an important role in classical applied probability theory, practical application remains essentially weak since all positive states are transient. A realistic modification which avoids this undesirable feature is to introduce immigration. In this paper we...

We derive criteria for assessing the recurrence and positive-recurrence of Markov branching processes with immigration. Although our method is designed to tackle the instantaneous immigration case investigated in Chen and Renshaw (1990), this new approach can also be applied to the stable...

Attention has recently focussed on stochastic population processes that can undergo total annihilation followed by immigration into state j at rate [alpha]j. The investigation of such models, called Markov branching processes with instantaneous immigration (MBPII), involves the study of...

Population systems are often subject to environmental noise, and our aim is to show that (surprisingly) the presence of even a tiny amount can suppress a potential population explosion. To prove this intrinsically interesting result, we stochastically perturb the multivariate deterministic...