Stochastic Model for Population Data Using a Birth–Death Diffusion Growth Rate Process

Abstract

One of the important functions of the
demographer is to provide information on the future population
which is important to plan for human activities. There is a
considerable interest in stochastic analogs of classical differences
and differential equations describing phenomena in theoretical
models involving population data structure. In this paper a
description of population data using a solution of stochastic
differential equation is considered. More specifically, the
population data process follows a Geometric progression with
growth rate follow a birth and death diffusion process is studied.
The mean and the variance approximation as well as the sample
path of such a process are also obtained. The model is applied to
the USA male population from 1900 to 1999 based on agespecific
death rates per 100,000 populations in specified group
computed by the direct method (Donna et al., 2001). The results
clearly demonstrated the appropriateness of the predicted
model.