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Bivariate stationary point processes, fundamental relations and first recurrence times

Published online by Cambridge University Press:  01 July 2016

T. K. M. Wisniewski
T. K. M. Wisniewski*
Affiliation:
Brunei University, Uxbridge, Middlesex
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Abstract

Various types of time and event sampling of a stationary and orderly bivariate point process are considered. Fundamental relations between inter-event intervals and the event counting process are derived. Relations between first forward recurrence times and their moments for different types of sampling are obtained.

Keywords

BIVARIATE POINT PROCESSRECURRENCE TIMESPALM KHINTCHINE FORMULAE

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 4 , Issue 2 , August 1972 , pp. 296 - 317
Copyright
Copyright © Applied Probability Trust 1972 

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References

Bartlett, M. S. (1967) Line processes and their spectral analysis. Proc. Fifth Berkeley Symp. on Math. Statist. and Prob. 3, 135–154.Google Scholar
Cox, D. R. and Lewis, P. A. W. (1966) The Statistical Analysis of Series of Events. Methuen, London.CrossRefGoogle Scholar
Cox, D. R. and Lewis, P. A. W. (1970) Multivariate point processes. Proc. Sixth Berkeley Symp. on Math. Statist. and Prob. Google Scholar
Cox, D. R. and Smith, W. L. (1954) On the superposition of renewal processes. Biometrika 41, 91–99.CrossRefGoogle Scholar
Daley, D. J. (1968) The correlation structure of the output process of some single server queueing systems. Ann. Math. Statist. 39, 1007–1019.Google Scholar
Khintchine, A. Y. (1960) Mathematical Methods in the Theory of Queueing. Griffin, London.Google Scholar
Lawrance, A. J. (1970) Selective interaction of a Poisson and renewal process: first-order stationary point results. J. Appl. Prob. 7, 359–372.Google Scholar
Leadbetter, M. R. (1966) On streams of events and mixtures of streams. J. R. Statist. Soc. B 28, 218–227.Google Scholar
Leadbetter, M. R. (1969) On the distribution of times between events in a stationary stream of events. J. R. Statist. Soc. B 31, 295–302.Google Scholar
Lewis, P. A. W. (1964) A branching Poisson process model for the analysis of computer failure patterns. J. R. Statist. Soc. B 26, 398–456.Google Scholar
McFadden, J. A. (1962) On the lengths of intervals in a stationary point process. J. R. Statist. Soc. B 24, 364–382.Google Scholar
McFadden, J. A. and Weissblum, W. (1963) Higher-order properties of a stationary point process. J. R. Statist. Soc. B 25, 413–431.Google Scholar
Marshall, A. W. and Olkin, I. (1967) A generalised bivariate exponential distribution. J. Appl. Prob. 4, 291–302.Google Scholar
Palm, C. (1943) Intensitätsschwankungen in Fernsprechverkehr. Ericsson Technics 44, 1–89.Google Scholar