Markov branching processes in a varying defective environment

C. Minuesa Abril, S. Sagitov

We study Markov branching processes describing populations of independently reproducing individuals in a varying environment. Each individual lives according to a time-dependent hazard rate, and its offspring number is governed by a possibly defective probability generating function which depends on the time. The defect of the offspring distribution at time t corresponds to the probability that an individual instantaneously sends the entire population into a special absorption state at time t.

The resulting processes have an enhanced state space with two absorbing states. We study the asymptotic behaviour of these processes, giving particular emphasis to the probabilities of absorption and of explosive growth.

Keywords: defective branching process, varying environment, generalized birth–death process, time change, limit theorems

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