Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T17:54:28.746Z Has data issue: false hasContentIssue false
  • English
  • Français

A characterization of the Poisson process

Published online by Cambridge University Press:  14 July 2016

S. M. Samuels
S. M. Samuels*
Affiliation:
Purdue University
Get access Rights & Permissions [Opens in a new window]

Abstract

Theorem: A necessary and sufficient condition for the superposition of two ordinary renewal processes to again be a renewal process is that they be Poisson processes.

A complete proof of this theorem is given; also it is shown how the theorem follows from the corresponding one for the superposition of two stationary renewal processes.

Keywords

POISSON PROCESSRENEWAL PROCESSSUPERPOSITIONSTATIONARY PROCESSPALM PROBABILITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 1 , March 1974 , pp. 72 - 85
Copyright
Copyright © Applied Probability Trust 1974 

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

[1] Çinlar, E. (1972) Superposition of point processes. Stochastic Point Processes (Ed. Lewis, P.). Wiley, New York. 549–606.Google Scholar
[2] Feller, W. (1971) An Introduction to Probability Theory and its Applications. Vol. II., 2nd ed. Wiley, New York.Google Scholar
[3] 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
[4] Mecke, J. (1967) Stationäre zufällige Masse auf lokalkompacten Abelschen Gruppen Z. Wahrscheinlichkeitsth. 9, 36–58.CrossRefGoogle Scholar
[5] Mecke, J. (1969) Verschärfung eines Satzes von McFadden Wiss. Z. Friedrich-Schiller-Univ. Jena/Thuringen 2, 387–392.Google Scholar
[6] Palm, C. (1943) Intensitätsschwankungen im Fernsprechverkehr Ericsson Technics 44, 1–89.Google Scholar
[7] Ryll-Nardzewski, C. (1961) Remarks on processes of calls. Proc. 4th Berkeley Symp. Math. Statist. Prob. II, 455–465.Google Scholar