Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

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Limit Theorems in Bellman–Harris Processes with Finites Second Moments
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Keywords

Bellman-Harris process
critical process
finite second moments
Proceso de Bellman-Harris
proceso crítico
segundos momentos finitos

How to Cite

Llinás Solano, H. (2010). Limit Theorems in Bellman–Harris Processes with Finites Second Moments. Revista De Matemática: Teoría Y Aplicaciones, 17(2), 103–120. https://doi.org/10.15517/rmta.v17i2.2123

Abstract

In this article are studied different theorems limits in a critical Bellman-Harris branching process with a only type of particle and with finite second moments. There were used two processes in order to figure out the limits as following as: “The condition of no extinction” and “The condition of extinction in the near future”. In the two previous processes is taken into account two different cases as: τi := dit y τi := di ± t, where t is a point of time and di ∈ (0,∞) are fixed for every i = 1, . . . , k. For the case where τi := dit, the Esty’s comparison lemma 2.3 is used to investigate the asymptotic behavior of the joint probability generating function F (s1, . . . , τk), for t → ∞; for the case τi := t + di, is not used. For this last case is founded another comparison lemma (lemma 4.3), that is the base to demonstrate the theorems limits if τi := t ± di.

https://doi.org/10.15517/rmta.v17i2.2123
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References

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Llinás, H. (2002) Grenzwertsaetze bei Kritischen Verzweiguns-prozessen. Tesis doctoral, Universidad de Mainz, Alemania.

Llinás, H.; Zapata, H. (2006) “Proceso crítico de Galton-Watson con segundos momentos infinitos”, Matemáticas: Enseñanza Universitaria (ERM) 14(2): 41–63.

Hurtado, J.; Llinás, H. (2007) “Teoremas límites en procesos de Galton-Watson con varianza finita”, Matemáticas: Enseñanza Universitaria (ERM) 15(2): 65–79

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