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Estimation of transition probabilities in a multiparticle semi-Markov system

Published online by Cambridge University Press:  14 July 2016

David Burman
David Burman*
Affiliation:
Bell Telephone Laboratories, Holmdel, New Jersey
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Abstract

Particles enter a finite-state system and move according to independent sample paths from a semi-Markov process. Strong limit theorems are developed for the ratio of the flow of particles from states i to j and the flow out of When the cumulative arrival of particles into the system up to time t, A (t) ∼ λtα, then a.s. When A (t)∼ λekt, then the flow between states must be normalized by the Laplace–Stieltjes transform of the conditional holding time distribution, in order to make the ratio an unbiased estimator of ρij.

Keywords

SEMI-MARKOV PROCESSESMULTIPARTICLE PROCESSESESTIMATION OF TRANSITION PROBABILITIESSTRONG LIMIT THEOREMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 4 , December 1976 , pp. 696 - 706
Copyright
Copyright © Applied Probability Trust 1976 

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References

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