TRANSIENT ANALYSIS OF LINEAR BIRTH–DEATH PROCESSES WITH IMMIGRATION AND EMIGRATION

Authors:
Yuxi Zheng;Xiuli Chao;Xiaomei Ji
Affiliations:
Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802;Department of Industrial Engineering, North Carolina State University, Raleigh, North Carolina 27695-7906, E-mail: xchao@ncsu.edu;Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
Venue:
Probability in the Engineering and Informational Sciences
Year:
2004

Citing 5
Cited 0

Linear birth and death models and associated Laguerre and Meixner polynomials

Journal of Approximation Theory
A course on integral equations

A course on integral equations
TRANSIENT ANALYSIS OF IMMIGRATION BIRTH–DEATH PROCESSES WITH TOTAL CATASTROPHES

Probability in the Engineering and Informational Sciences
Theory, Volume 1, Queueing Systems

Theory, Volume 1, Queueing Systems
Introduction to Probability Models, Ninth Edition

Introduction to Probability Models, Ninth Edition

Quantified Score

Hi-index	0.00

Visualization

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.