Diffusion Approximation of an Array of Controlled Branching Processes

2012 ◽  
Vol 14 (3) ◽  
pp. 843-861 ◽  
Author(s):  
Miguel González ◽  
Inés M. del Puerto
Keyword(s):  
Diffusion Approximation ◽  
Branching Processes ◽  
Controlled Branching Processes

On the class of controlled branching processes with random control functions

2002 ◽  
Vol 39 (4) ◽  
pp. 804-815 ◽  
Author(s):  
M. González ◽  
M. Molina ◽  
I. Del Puerto
Keyword(s):  
Population Size ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Control Functions ◽  
Controlled Branching Processes ◽  
Necessary And Sufficient ◽  
Random Control

In this paper, the class of controlled branching processes with random control functions introduced by Yanev (1976) is considered. For this class, necessary and sufficient conditions are established for the process to become extinct with probability 1 and the limit probabilistic behaviour of the population size, suitably normed, is investigated.

Controlled Branching Processes

1974 ◽  
Vol 19 (1) ◽  
pp. 14-24 ◽  
Author(s):  
B. A. Sevast’yanov ◽  
A. M. Zubkov
Keyword(s):  
Branching Processes ◽  
Controlled Branching Processes

Limit theorems for some functionals of certain Galton-Watson branching processes

1974 ◽  
Vol 6 (2) ◽  
pp. 309-321 ◽  
Author(s):  
Torgny Lindvall
Keyword(s):  
Diffusion Approximation ◽  
Limit Theorems ◽  
Branching Processes

This paper extends the Feller-Jiřina theorem on the diffusion approximation of Galton-Watson branching processes with reproduction mean close to one, and limit theorems are obtained for several functionals of such processes.

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

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.

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