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Further results on ASTA for general stationary processes and related problems

Published online by Cambridge University Press:  14 July 2016

Masakiyo Miyazawa  and
Ronald W. Wolff
Masakiyo Miyazawa*
Affiliation:
Science University of Tokyo
Ronald W. Wolff*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Department of Information Sciences, Science University of Tokyo, Noda-city, Chiba 278, Japan.
∗∗ Postal address: Department of IEOR, University of California, Berkeley, CA 94720, USA.
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Abstract

We consider the equivalence of state probabilities of a general stationary process at an arbitrary time and at embedded epochs of a given point process, which is called ASTA (Arrivals See Time Averages). By using an event-conditonal intensity, we give necessary and sufficient conditions for ASTA for a large class of state sets, which determines a state distribution. We do not need any additional assumptions except that the general process has left-hand limits at all points of time. Especially, for a stationary pure-jump process with a point process, ASTA is obtained for all state sets. As an application of those results, Anti-PASTA is obtained for a pure-jump Markov process and a certain class of GSMP (Generalized Semi-Markov Processes), where Anti-PASTA means that ASTA implies that the arrival process is Poisson.

Keywords

QUEUESPURE-JUMP PROCESSGSMPPASTAANTI-PASTACONDITIONAL INTENSITYPOINT PROCESSPALM DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 4 , December 1990 , pp. 792 - 804
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

Part of this work was done when R. W. Wolff visited the Science University of Tokyo in 1989.

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