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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Main Author: Llin?s Solano, Humberto
Format: Artículo
Language: Español
Published: 2015
Online Access: http://revistas.ucr.ac.cr/index.php/matematica/article/view/2123
http://hdl.handle.net/10669/12974
Summary: 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 $i := \tau ? di$.