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An invariance property of Poisson processes

Published online by Cambridge University Press:  14 July 2016

Mark Brown
Mark Brown*
Affiliation:
Cornell University
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Extract

In this paper we shall investigate point processes generated by random variables of the form 〈gi (Ti ]), i=± 1, ± 2, … 〉, where 〈Ti, i= ± 1, … 〉 is the set of arrival times from a (not necessarily homogeneous) Poisson process or mixture of Poisson processes, and 〈gi, i = ± 1, … 〉 is an independently and identically distributed (i.i.d.) or interchangeable sequence of random functions, independent of 〈Ti 〉.

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 6 , Issue 2 , August 1969 , pp. 453 - 458
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

[1] Brown, M. (1968) Some results on a traffic model of Renyi. J. Appl. Prob. 6, 293–300.CrossRefGoogle Scholar
[2] Brown, M. (1968) An invariance property of Poisson processes arising in traffic flow theory. Stanford University Technical Report. Google Scholar
[3] Brown, M. and Ross, S. (1968), Some results on infinite server Poisson queues. Cornell and University of California Technical Reports. Google Scholar
[4] Doob, J. L. (1953) Stochastic Processes. John Wiley, New York.Google Scholar
[5] Hewitt, E. and Savage, L. J. (1955) Symmetric measures on cartesian products. Trans. Amer. Math. Soc. 80, 470–501.Google Scholar
[6] Karlin, S. (1966) A First Course in Stochastic Processes. Academic Press, New York and London.Google Scholar
[7] Renyi, A. (1964) On two mathematical models of the traffic on a divided highway. J. Appl. Prob. 1, 311–320.Google Scholar
[8] Ryll-Nardzewski, C. (1954) Remarks on the Poisson stochastic process (III), Studia Math. 14, 124–128.CrossRefGoogle Scholar