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

In this article are studied different theorems limits in a criticalBellman-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 ext...

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Autor Principal: Llinás Solano, Humberto Artículo Español 2015 http://revistas.ucr.ac.cr/index.php/matematica/article/view/2123 http://hdl.handle.net/10669/12974
Sumario: In this article are studied different theorems limits in a criticalBellman-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: $i := dit$  y $i := di ± \tau$, where t is a point of time and $d_i\varepsilon (0,\infty )$ are fixed for every $i = 1, . . . ,k$. For the case where $i := di\tau$, the Esty’s comparison lemma 2.3 is used to investigate the asymptotic behavior of the joint probability generating function F$F(s_1,...,\tau_k)$, for $t\longrightarrow \infty$; for the case  $i := \tau + di$ 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 $i := \tau ± di$.