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Birth-and-death processes on the integers with phases and general boundaries

Published online by Cambridge University Press:  14 July 2016

Bruce Hajek
Bruce Hajek*
Affiliation:
University of Illinois at Urbana-Champaign
*
∗Postal address: Coordinated Science Laboratory, 1101 W. Springfield, Urbana, IL 61801, U.S.A.
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Abstract

The invariant probability distribution is found for a class of birth-and-death processes on the integers with phases and one or two boundaries. The invariant vector has a matrix geometric form and is found by solving a non-linear matrix equation and then finding an invariant probability distribution on the boundary states. Levy's concept of watching a Markov process in a subset is used to naturally decouple the computation of distributions on the boundary and interior states.

Keywords

MARKOV PROCESS WITH PHASESPROBABILITY DISTRIBUTIONS OF PHASE TYPECOMPUTATIONAL PROBABILITYMARKOV PROCESSES WATCHED IN A SETQUASI-BIRTH-AND-DEATH PROCESSES
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 488 - 499
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

This research was supported by the Naval Research Laboratory under Contract U.S. NAVY N00014-80-C-0802.

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