Abstract
Very few stochastic systems are known to have closed-form
transient solutions. In this article we consider an immigration
birth and death population process with total catastrophes and
study its transient as well as equilibrium behavior. We obtain
closed-form solutions for the equilibrium distribution as well
as the closed-form transient probability distribution at any
time t ≥ 0. Our approach involves solving ordinary
and partial differential equations, and the method of characteristics
is used in solving partial differential equations.
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability
Cited by
37 articles.
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