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More predictable, less predictable and stable counting processes

Part of: Stochastic processes Sufficiency and information

Published online by Cambridge University Press:  14 July 2016

Nader Ebrahimi
Nader Ebrahimi*
Affiliation:
Northern Illinois University
*
∗ Postal address: Division of Statistics, Northern Illinois University, DeKalb, IL 60115–2854, USA.
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Abstract

In a counting process considered at time t the focus is often on the length of the current interarrival time, whereas points in the past may be said to constitute information about the process. The paper introduces new concepts on how to quantify predictability of the future behavior of counting processes based on the past information and considers then situations in which the future points become more (or less) predictable. Various properties of our proposed concepts are studied and applications relevant to the reliability of repairable systems are given.

Keywords

POISSON PROCESSRENEWAL PROCESSSEMI-MARKOV PROCESSDELAYED RENEWAL PROCESSIFR DISTRIBUTIONMINIMAL REPAIR

MSC classification

Primary: 62B10: Information-theoretic topics
Secondary: 60G15: Gaussian processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 2 , June 1993 , pp. 341 - 352
Copyright
Copyright © Applied Probability Trust 1993 

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References

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