Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-12-02T22:23:27.518Z Has data issue: false hasContentIssue false
  • English
  • Français

On the times of births in a linear birthprocess

Published online by Cambridge University Press:  09 April 2009

Marcel F. Neuts  and
Sidney I. Resnick
Marcel F. Neuts
Affiliation:
Cornell University
Sidney I. Resnick
Affiliation:
Purdue University
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If S1, S2,… are the times of successive births in a pure birth-process with linear birthrate and i > 0 individuals initially, then given that there are k > 0 births in (0, t), the random variables eλS1—1, eλS2−1,λS1−1 are distributed (conditionally) like the order statistics of k independent random variables, all uniformly distributed on the interval (0, eλt–1), regardless of the initial population size. A similar property holds for the pure death process.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 12 , Issue 4 , November 1971 , pp. 473 - 475
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Karlin, Samuel, A First Course in Stochastic Processes (Academic Press, New York and London, 1966).Google Scholar