C. Minuesa Abril, G. Kersting
The Galton-Watson process is a discrete-time Markov chain which models populations in which each individual reproduces independently of the others according to some probability law.
In this talk, we present a generalization of the previous model which consists in letting the reproduction law to be a possible defective probability distribution and change over the time. The resulting process is called defective branching processes in varying environment. The defect of the offspring distribution at generation n is interpreted as the probability that a particle at generation n sends the process to an absorbing graveyard state, where it stays forever. These processes have an enhanced state space with two absorbing states. We study some results regarding their asymptotic behaviour. We establish the almost sure convergence of the process to a random variable and then, we provide necessary and sufficient conditions for having the duality extinction - absorption at the graveyard state.
Keywords: defective distribution, absorption, branching process, graveyard state, varying environment
Scheduled
GT15.PROCEST3 Invited Session
November 9, 2023 3:30 PM
HC3: Canónigos Room 3