\title{Transient analysis of linear birth-death processes\\
with immigration and emigration}



Yuxi Zheng, Xiuli Chao, Xiaomei Ji 



\begin{abstract}

Birth-death processes with immigration and emigration are 
major models in the study of population process of 
biological and ecological systems and their transient 
analysis is important in the understanding of the 
structural behavior of such systems.  However,  analytic 
transient solution for such systems has been derived only 
for some special cases of such processes. In this paper we 
present a transient analysis for this process. For the 
general case we present a Volterra type integral equation 
for the chance of extinction and an explicit formula for 
the z-transform of the transient distribution. These 
results also allow us to obtain closed form solutions 
for the transient behavior of several special cases 
that have not been previously solved in the literature.  

\end{abstract}