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A note on three stochastic processes with immigration

Published online by Cambridge University Press:  17 February 2009

J. Gani  and
L. Stals
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Abstract

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Three stochastic processes, the birth, death and birth-death processes, subject to immigration can be decomposed into the sum of each process in the absence of immigration and anindependent process. We examine these independent processes through their probability generating functions (pgfs) and derive their expectations.

Keywords

birthdeath and birth-death processes with immigrationprobability generating functions (pgfs)expectation.
Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 3 , January 2007 , pp. 409 - 418
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Abramowitz, M. and Stegun, I. A., Handbook of mathematical functions (US National Bureau of Standards, Washington, D.C., 1964).Google Scholar
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[3]Cox, D. R. and Miller, H. D., The theory of stochastic processes (Methuen, London, 1965).Google Scholar