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An inhomogeneous controlled branching process∗

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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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Authors and Affiliations

  1. Department of Mathematics, University of Extremadura, Avda Elvas s/n, 06006, Badajoz, Spain

    Miguel González, Carmen Minuesa, Manuel Mota, Inés del Puerto & Alfonso Ramos

  2. Institute of Advanced Scientific Computing (ICCAEx), University of Extremadura, Avda Elvas s/n, 06006, Badajoz, Spain

    Miguel González, Carmen Minuesa, Manuel Mota & Inés del Puerto

Authors
  1. Miguel González
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  2. Carmen Minuesa
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  3. Manuel Mota
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  4. Inés del Puerto
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  5. Alfonso Ramos
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Corresponding author

Correspondence to Miguel González.

Additional information

∗ 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

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