O PROCESSO DE RENOVAÇÃO GENERALIZADO DE KENDALL E A NECESSIDADE DA CONSTRUÇÃO DE PROCESSOS ESTOCÁSTICOS DE DIFUSÃO

Abstract

The purpose of this paper is to present some problems concerning the construction of stochastic models for population growth and the dificulties yet existing in this field in respect to have more realistic and elabored models for describing the population dynamics. With this in mind, we introduced the Linear Homogeneous Birth and Death Process and after analysing it as its limitations we presented the Generalized Birth and Death Process, due to Kendall. Since this last metioned process involves complicated computional formulas we introduced, as an approximation, the concept of a Difusion Process, showing however that Difusion Process anaJogue to the Generalized Birth and Death Process can not yet be obtained due to theoretical dificulties. Thus we are left with the Difusion Process analogue to the Homogeneous Birth and Death Process. The paper contains also a comparison between the expected results under the Homogeneous Birth and Death Process and the correspondente Difusion Process.