The Markov branching process with density-independent catastrophes. II. The subcritical and critical cases

Abstract

This paper continues the study initiated in [10] of the Markov branching process (MBP) subject to an independent Poisson process of catastrophe times at which the population size is reduced by random decrements whose distribution is independent of the current population size. More generally, let (Xt:t ≥ 0) be the Feller process on the non-negative integers ℕ+ having the generator