An inhomogeneous controlled branching process(au)

作者：Gonzalez Miguel^*; Minuesa Carmen; Mota Manuel; del Puerto Ines; Ramos Alfonso

来源：Lithuanian Mathematical Journal, 2015, 55(1): 61-71.

DOI：10.1007/s10986-015-9265-0

• branching process
• controlled branching process
• inhomogeneous branching process
• extinction probability
• asymptotic behavior

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.

• 出版日期2015-1