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Geometric Markov chains

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

William Rising
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Abstract

A generalization of the familiar birth–death chain, called the geometric chain, is introduced and explored. By the introduction of two families of parameters in addition to the infinitesimal birth and death rates, the geometric chain allows transitions beyond the nearest neighbor, but is shown to retain the simple computational formulas of the birth–death chain for the stationary distribution and the expected first-passage times between states. It is also demonstrated that even when not reversible, a reversed geometric chain is again a geometric chain.

Keywords

REVERSIBILITYSTATIONARY DISTRIBUTIONSEXPECTED FIRST-PASSAGE TIMES

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 2 , June 1995 , pp. 349 - 374
Copyright
Copyright © Applied Probability Trust 1995 

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References

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