Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-26T09:49:19.818Z Has data issue: false hasContentIssue false
  • English
  • Français

Some non-stationary point processes with stationary forward recurrence time distribution

Published online by Cambridge University Press:  14 July 2016

Mats Rudemo
Mats Rudemo*
Affiliation:
The Royal Veterinary and Agricultural University, Copenhagen
Get access Rights & Permissions [Opens in a new window]

Abstract

Examples are given of point processes that are non-stationary but have stationary forward recurrence time distributions. They are obtained by modification of stationary Poisson and renewal processes.

Keywords

STATIONARITY OF POINT PROCESSESFORWARD RECURRENCE TIME
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 167 - 169
Copyright
Copyright © Applied Probability Trust 1975 

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

Chung, K. L. (1972) Crudely stationary counting processes. Amer. Math. Monthly 79, 867–877.CrossRefGoogle Scholar
Goldman, J. R. (1967) Stochastic point processes: Limit theorems. Ann. Math. Statist. 38, 771–779.CrossRefGoogle Scholar
Lawrance, A. J. (1970) Selective interaction of a Poisson and renewal process: First-order stationary point results. J. Appl. Prob. 7, 359–372.CrossRefGoogle Scholar
Lawrance, A. J. (1974) Theory of interevent interval distributions for stationary point processes. Information and Control. 25, 299–316.CrossRefGoogle Scholar
Leadbetter, M. R. (1966) On streams of events and mixtures of streams. J. R. Statist. Soc. B 28, 218–227.Google Scholar
Lee, P. M. (1968) Some examples of infinitely divisible point processes. Studia Sci. Math. Hung. 3, 219–224.Google Scholar
Moran, P. A. P. (1967) A non-Markovian quasi-Poisson process. Studia Sci. Math. Hung. 2, 425–429.Google Scholar
Rényi, A. (1967) Remarks on the Poisson process. Studia Sci. Math. Hung. 2, 119–123.Google Scholar