On the Controlled Galton-Watson Process with Random Control Function

Asymptotic behaviour of critical controlled branching processes with random control functions

“…, which is equivalent to mk −1 ε(k); this is intuitively interpreted as the expected growth rate per individual when, in a certain generation, there are k individuals. In order to obtain conditions for the almost-sure extinction, different possible behaviours for the sequence {τ (k)} k≥1 , relative to 1, have been considered in [4]. In particular, the cases lim sup k→∞ τ (k) < 1 and lim inf k→∞ τ (k) > 1, respectively called subcritical and supercritical, have been investigated.…”

“…Several questions concerning this control model have been investigated in [1], [3], [15], and [19]. Recently (see [4], [5], [6], and [7]), it has been studied in the framework of asymptotically linear growth of the mathematical expectations of the control variables. In this paper, we continue the research into this class of branching models and, in a critical case, we investigate some pertinent questions that have not previously been considered in the literature.…”

On asymptotic posterior normality for controlled branching processes

“…For CBP, some results about its extinction probability and limiting behaviour have been investigated in [1,3,4,[5][6][7][8][9]. In these works it is remarkable the role played by the offspring mean, m = E[X 0,1 ], in the behaviour of the CBPs.…”

Analysis of a Recurrence Related to Critical Nonhomogeneous Branching Processes

“…Yanev [14] assumed also a random environment. Gonzales et al [16,17] investigated the model (1) when the means of the RCF have a linear growth.…”