Hostname: page-component-cb9f654ff-mnl9s Total loading time: 0 Render date: 2025-08-21T15:21:30.642Z Has data issue: false hasContentIssue false
  • English
  • Français

Ergodicity and identifiability for random translations of stationary point processes

Published online by Cambridge University Press:  14 July 2016

Toshio Mori
Toshio Mori*
Affiliation:
Yokohama City University
Get access Rights & Permissions [Opens in a new window]

Abstract

A bivariate point process consisting of an original stationary point process and its random translation is considered. Westcott's method is applied to show that if the original point process is ergodic then the bivariate point process is also ergodic. This result is applied to an identification problem of the displacement distribution. It is shown that if the spectrum of the original process is the real line then the displacement distribution is identifiable from almost every sample realisation of the bivariate process.

Keywords

STATIONARY POINT PROCESSRANDOM TRANSLATION OF POINT PROCESSIDENTIFIABILITY FOR POINT PROCESSGI/G/∞ QUEUE

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 4 , December 1975 , pp. 734 - 743
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.)

Article purchase

Temporarily unavailable

References

Billingsley, P. (1965) Ergodic Theory and Information. Wiley, New York.Google Scholar
Brillinger, D. R. (1974) Cross-spectral analysis of processes with stationary increments including the stationary G/G/8 queue. Ann. Prob. 2, 815–827.Google Scholar
Brown, M. (1970) An M/G/8 estimation problem. Ann. Math. Statist. 41, 651–654.CrossRefGoogle 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. (1971) Weakly stationary point processes and random measures. J. R. Statist. Soc. B 33, 406–425.Google Scholar
Milne, R. K. (1970) Identifiability for random translations of Poisson processes. Z. Wahrscheinlichkeitsth. 15, 195–201.CrossRefGoogle Scholar
Ryll-Nardzewski, C. (1960) Remarks on processes of calls. Proc. 4th Berkeley Symp. Math. Statist. Prob. 2, 455–465.Google Scholar
Vere-Jones, D. (1968) Some applications of probability generating functionals to the study of input-output streams. J. R. Statist. Soc. B 30, 321–333.Google Scholar
Vere-Jones, D. (1974) An elementary approach to the spectral theory of stationary random measures. In Stochastic Geometry, ed. Harding, E. F. and Kendall, D. G., Wiley, New York.Google Scholar
Westcott, M. (1971) On existence and mixing results for cluster point processes. J. R. Statist. Soc. B 33, 290–300.Google Scholar
Westcott, M. (1972) The probability generating functional. J. Austral. Math. Soc. 14, 448–466.Google Scholar