An inhomogeneous controlled branching process
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.
Cite
@article{arxiv.2401.16010,
title = {An inhomogeneous controlled branching process},
author = {Miguel González and Carmen Minuesa and Manuel Mota and Inés del Puerto and Alfonso Ramos},
journal= {arXiv preprint arXiv:2401.16010},
year = {2024}
}
Comments
15 pages. This is a plain preprint version of the article that was published, after peer review, and is subject to Springer Nature's terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s10986-015-9265-0