Limiting distribution for subcritical controlled branching processes with random control function

2004 ◽  
Vol 67 (3) ◽  
pp. 277-284 ◽  
Author(s):  
M. González ◽  
M. Molina ◽  
I. del Puerto
Keyword(s):  
Control Function ◽  
Branching Processes ◽  
Limiting Distribution ◽  
Controlled Branching Processes ◽  
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

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 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.

scholarly journals Asymptotic behaviour of critical controlled branching processes with random control functions

2005 ◽  
Vol 42 (2) ◽  
pp. 463-477 ◽  
Author(s):  
M. González ◽  
M. Molina ◽  
I. del Puerto
Keyword(s):  
Asymptotic Behaviour ◽  
Critical Case ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Control Functions ◽  
Limiting Behaviour ◽  
Controlled Branching Processes ◽  
Random Control

In this paper, we investigate the asymptotic behaviour of controlled branching processes with random control functions. In a critical case, we establish sufficient conditions for both their almost-sure extinction and for their nonextinction with a positive probability. For some suitably chosen norming constants, we also determine different kinds of limiting behaviour for this class of processes.

scholarly journals Asymptotic behaviour of critical controlled branching processes with random control functions

2005 ◽  
Vol 42 (02) ◽  
pp. 463-477 ◽  
Author(s):  
M. González ◽  
M. Molina ◽  
I. del Puerto
Keyword(s):  
Asymptotic Behaviour ◽  
Critical Case ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Control Functions ◽  
Limiting Behaviour ◽  
Controlled Branching Processes ◽  
Random Control

In this paper, we investigate the asymptotic behaviour of controlled branching processes with random control functions. In a critical case, we establish sufficient conditions for both their almost-sure extinction and for their nonextinction with a positive probability. For some suitably chosen norming constants, we also determine different kinds of limiting behaviour for this class of processes.

On the class of controlled branching processes with random control functions

2002 ◽  
Vol 39 (04) ◽  
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.

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 Genealogy for supercritical branching processes

2006 ◽  
Vol 43 (04) ◽  
pp. 1066-1076 ◽  
Author(s):  
Andreas Nordvall Lagerås ◽  
Anders Martin-Löf
Keyword(s):  
Marginal Distribution ◽  
Branching Processes ◽  
Limiting Distribution ◽  
Random Trees ◽  
Limiting Distributions ◽  
Marginal Distributions ◽  
Special Cases ◽  
Supercritical Branching Processes

We study the genealogy of so-called immortal branching processes, i.e. branching processes where each individual upon death is replaced by at least one new individual, and conclude that their marginal distributions are compound geometric. The result also implies that the limiting distributions of properly scaled supercritical branching processes are compound geometric. We exemplify our results with an expression for the marginal distribution for a class of branching processes that have recently appeared in the theory of coalescent processes and continuous stable random trees. The limiting distribution can be expressed in terms of the Fox H-function, and in special cases by the Meijer G-function.

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