M. González Velasco, G. Kersting, C. Minuesa Abril, I. M. del Puerto García
The model introduced is this work is a modification of the standard branching process in which the reproduction law is inhomogeneous and moreover an inhomogeneous immigration is allowed. That is, the reproduction and immigration laws may vary along generations. This exibility makes the process more suitable to model real populations due to the fact that the stability in the reproductive capacity and in the immigration laws are not usually fulfilled. In this setting, we study the extinction problem and provide a necessary and sufficient condition for the certain extinction of these populations. The asymptotic behaviour of the model is analysed for those processes with critical offspring distributions, according with the classification established in Kersting (2017), and when the immigration means stabilize to a positive value. More specifically, we establish that the asymptotic distribution of the process -under a suitable normalization- belongs to the Gamma distribution family.
Palabras clave / Keywords: ...
Programado
Sesión 1 Premio Ramiro Melendreras
29 de mayo de 2018 09:10
Sala Cristal
