Transient analysis of Linear birth-death processes with immigration and emigration

Yuxi Zheng, Xiuli Chao, J. I. Xiaomei

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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 In this article, we provide an alternative approach: the method of characteristics. This method yields a Volterratype 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.

Original languageEnglish (US)
Pages (from-to)141-159
Number of pages19
JournalProbability in the Engineering and Informational Sciences
Volume18
Issue number2
DOIs
Publication statusPublished - May 7 2004

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering

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