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arXiv · 2401.16010

An inhomogeneous controlled branching process

Miguel González·Carmen Minuesa·Manuel Mota·Inés del Puerto·Alfonso Ramos
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Abstract

A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the transition probabilities are non-stationary. Under not too restrictive hypotheses, this model presents the classical duality of branching processes: either becomes extinct almost surely or grows to infinity. Sufficient conditions for the almost sure extinction and for a positive probability of indefinite growth are provided. Finally rates of growth of the process provided the non-extinction are studied.

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Miguel González, Carmen Minuesa, Manuel Mota, Inés del Puerto, Alfonso Ramos. 2024-01-29. An inhomogeneous controlled branching process. https://doi.org/10.1007/s10986-015-9265-0

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