An inhomogeneous controlled branching process∗

• DOI: 10.1007/s10986-015-9265-0
• Publication Date: 2015-03-03T22:01:48Z
• Authors: Miguel González; Carmen Minuesa; Manuel Mota; Inés del Puerto; Alfonso Ramos
• Keywords: Branching process; Branching (polymer chemistry)

Comment: 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<br/>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.<br/>