Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-30T20:25:10.222Z Has data issue: false hasContentIssue false

Some multivariate generalizations of results in univariate stationary point processes

Published online by Cambridge University Press:  14 July 2016

Mark Berman*
Affiliation:
Imperial College, London

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1977 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Çinlar, E. (1969) Markov renewal theory. Adv. Appl. Prob. 1, 123187.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, 401448.Google Scholar
Daley, D. J. and Milne, R. K. (1975) Orderliness, intensities and Palm–Khinchin equations for multivariate point processes. J. Appl. Prob. 12, 383389.Google Scholar
Leadbetter, M. R. (1971) On basic results of point process theory. Proc. 6th Berkeley Symp. Math. Statist. Prob. 3, 449462.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