scholarly journals Estimation of the offspring mean in a controlled branching process with a random control function

2007 ◽  
Vol 117 (7) ◽  
pp. 928-946 ◽  
Author(s):  
T.N. Sriram ◽  
A. Bhattacharya ◽  
M. González ◽  
R. Martínez ◽  
I. del Puerto
Keyword(s):  
Branching Process ◽  
Control Function ◽  
Random Control

On the geometric growth in controlled branching processes with random control function

2003 ◽  
Vol 40 (04) ◽  
pp. 995-1006 ◽  
Author(s):  
M. González ◽  
M. Molina ◽  
I. del Puerto
Keyword(s):  
Branching Process ◽  
Control Function ◽  
Branching Processes ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Limit Behaviour ◽  
Controlled Branching Processes ◽  
Necessary And Sufficient ◽  
Random Control ◽  
Geometric Growth

The limit behaviour of a controlled branching process with random control function is investigated. A necessary condition and a sufficient condition for the geometric growth of such a process are established by considering the L 1-convergence. Finally, taking into account the classical X log+ X criterion in branching processes, a necessary and sufficient condition is provided.

On the geometric growth in controlled branching processes with random control function

2003 ◽  
Vol 40 (4) ◽  
pp. 995-1006 ◽  
Author(s):  
M. González ◽  
M. Molina ◽  
I. del Puerto
Keyword(s):  
Branching Process ◽  
Control Function ◽  
Branching Processes ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Limit Behaviour ◽  
Controlled Branching Processes ◽  
Necessary And Sufficient ◽  
Random Control ◽  
Geometric Growth

The limit behaviour of a controlled branching process with random control function is investigated. A necessary condition and a sufficient condition for the geometric growth of such a process are established by considering the L1-convergence. Finally, taking into account the classical X log+X criterion in branching processes, a necessary and sufficient condition is provided.

On the Controlled Galton-Watson Process with Random Control Function

2004 ◽  
Vol 121 (5) ◽  
pp. 2629-2635 ◽  
Author(s):  
M. González ◽  
M. Molina ◽  
I. del Puerto
Keyword(s):  
Control Function ◽  
Watson Process ◽  
Random Control

scholarly journals On L 2 -convergence of controlled branching processes with random control function

Bernoulli ◽  
2005 ◽  
Vol 11 (1) ◽  
pp. 37-46 ◽  
Author(s):  
Miguel González ◽  
Manuel Molina ◽  
Inés Del Puerto
Keyword(s):  
Control Function ◽  
Branching Processes ◽  
Controlled Branching Processes ◽  
Random Control

scholarly journals A Predator–Prey Two-Sex Branching Process

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1408
Author(s):  
Cristina Gutiérrez ◽  
Carmen Minuesa
Keyword(s):  
Stochastic Process ◽  
Branching Process ◽  
Sufficient Conditions ◽  
Predator Population ◽  
Predator Prey ◽  
Control Functions ◽  
Branching Model ◽  
Necessary And Sufficient ◽  
Number Of Individuals ◽  
Random Control

In this paper, we present the first stochastic process to describe the interaction of predator and prey populations with sexual reproduction. Specifically, we introduce a two-type two-sex controlled branching model. This process is a two-type branching process, where the first type corresponds to the predator population and the second one to the prey population. While each population is described via a two-sex branching model, the interaction and survival of both groups is modelled through control functions depending on the current number of individuals of each type in the ecosystem. In view of their potential for the conservation of species, we provide necessary and sufficient conditions for the ultimate extinction of both species, the fixation of one of them and the coexistence of both of them. Moreover, the description of the present predator–prey two-sex branching process on the fixation events can be performed in terms of the behaviour of a one-type two-sex branching process with a random control on the number of individuals, which is also introduced and analysed.

scholarly journals Rates of Growth in a Class of Homogeneous Multidimensional Markov Chains

2006 ◽  
Vol 43 (01) ◽  
pp. 159-174 ◽  
Author(s):  
M. González ◽  
R. Martínez ◽  
M. Mota
Keyword(s):  
Markov Chains ◽  
Nonnegative Integer ◽  
Branching Process ◽  
Critical Case ◽  
Branching Processes ◽  
Positive Probability ◽  
Multitype Branching Process ◽  
Rates Of Growth ◽  
Theoretical Results ◽  
Random Control

We investigate the asymptotic behaviour of homogeneous multidimensional Markov chains whose states have nonnegative integer components. We obtain growth rates for these models in a situation similar to the near-critical case for branching processes, provided that they converge to infinity with positive probability. Finally, the general theoretical results are applied to a class of controlled multitype branching process in which random control is allowed.

scholarly journals Rates of Growth in a Class of Homogeneous Multidimensional Markov Chains

2006 ◽  
Vol 43 (1) ◽  
pp. 159-174 ◽  
Author(s):  
M. González ◽  
R. Martínez ◽  
M. Mota
Keyword(s):  
Markov Chains ◽  
Nonnegative Integer ◽  
Branching Process ◽  
Critical Case ◽  
Branching Processes ◽  
Positive Probability ◽  
Multitype Branching Process ◽  
Rates Of Growth ◽  
Theoretical Results ◽  
Random Control

We investigate the asymptotic behaviour of homogeneous multidimensional Markov chains whose states have nonnegative integer components. We obtain growth rates for these models in a situation similar to the near-critical case for branching processes, provided that they converge to infinity with positive probability. Finally, the general theoretical results are applied to a class of controlled multitype branching process in which random control is allowed.

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