Abstract
We consider a discrete-time branching process in which the offspring distribution is generation-dependent and the number of reproductive individuals is controlled by a random mechanism. This model is a Markov chain, but, in general, the transition probabilities are nonstationary. Under not too restrictive hypotheses, this model presents the classical duality of branching processes: it either becomes extinct or grows to infinity. Sufficient conditions for the almost sure extinction and for a positive probability of indefinite growth are given. Finally, the rates of growth of the process are studied, provided that there is no extinction.
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∗ This research was supported by the Ministerio de Economía y Competitividad and the FEDER through the Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnolólgica, grant MTM2012-31235.
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González, M., Minuesa, C., Mota, M. et al. An inhomogeneous controlled branching process∗ . Lith Math J 55, 61–71 (2015). https://doi.org/10.1007/s10986-015-9265-0
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DOI: https://doi.org/10.1007/s10986-015-9265-0
Keywords
- branching process
- controlled branching process
- inhomogeneous branching process
- extinction probability
- asymptotic behavior