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Some multivariate generalizations of results in univariate stationary point processes

Published online by Cambridge University Press:  14 July 2016

Mark Berman
Mark Berman*
Affiliation:
Imperial College, London
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Abstract

Some relationships are derived between the asynchronous and partially synchronous counting and interval processes associated with a multivariate stationary point process. A few examples are given to illustrate some of these relationships.

Keywords

POINT PROCESSMULTIVARIATE POINT PROCESSSTATIONARITYMARKOV RENEWAL PROCESSORDERLINESSSTRONG ORDERLINESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 4 , December 1977 , pp. 748 - 757
Copyright
Copyright © Applied Probability Trust 1977 

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References

Çinlar, E. (1969) Markov renewal theory. Adv. Appl. Prob. 1, 123–187.Google Scholar
Cox, D. R. (1962) Renewal Theory. Methuen, London.Google Scholar
Cox, D. R. and Lewis, P. A. W. (1966) The Statistical Analysis of Series of Events. Methuen, London.Google Scholar
Cox, D.R. and Lewis, P. A. W. (1972) Multivariate point processes. Proc. 6th Berkeley Symp. Math. Statist. Prob. 3, 401–448.Google Scholar
Daley, D. J. and Milne, R. K. (1975) Orderliness, intensities and Palm–Khinchin equations for multivariate point processes. J. Appl. Prob. 12, 383–389.Google Scholar
Leadbetter, M. R. (1971) On basic results of point process theory. Proc. 6th Berkeley Symp. Math. Statist. Prob. 3, 449–462.Google Scholar
Oakes, D. (1972) Semi-Markov Representations of Some Stochastic Point Processes. , Imperial College, University of London.Google Scholar
Widder, D. V. (1946) The Laplace Transform. Princeton University Press, Princeton, N.J.Google Scholar