Author:
Zheng* Yuxi,Chao[dagger] Xiuli,Ji Xiaomei
Abstract
Linear birth–death processes with immigration
and emigration are major models in the study of population processes of
biological and ecological systems, and their transient analysis is
important in the understanding of the structural behavior of such
systems. The spectral method has been widely used for solving these
processes; see, for example, Karlin and McGregor [11]. In this article, we provide an
alternative approach: the method of characteristics. This method yields
a Volterra-type integral equation for the chance of extinction and an
explicit formula for the z-transform of the transient
distribution. These results allow us to obtain closed-form solutions
for the transient behavior of several cases that have not been
previously explicitly presented in the literature.
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability
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