Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-28T20:12:47.474Z Has data issue: false hasContentIssue false
  • English
  • Français

A convergence theorem for parities in a birth-and-death process

Published online by Cambridge University Press:  14 July 2016

I. W. Saunders
I. W. Saunders*
Affiliation:
C.S.I.R.O. Division of Mathematics and Statistics, Canberra
Get access Rights & Permissions [Opens in a new window]

Abstract

The parity of an individual in a population process is the number of offspring that individual has produced. If Nk(t) is the number of individuals of parity k at time t in a birth-and-death process and we show that, conditional on N(t)→ ∞,

Keywords

BIRTH-AND-DEATH PROCESSPARITYALMOST SURE CONVERGENCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 2 , June 1976 , pp. 231 - 238
Copyright
Copyright © Applied Probability Trust 1976 

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

Feller, W. (1968), (1971) An Introduction to Probability Theory and its Applications. Vol. I, 3rd edn. and Vol. II, 2nd edn. Wiley, New York.Google Scholar
Gani, J. and Saunders, I. W. (1976) On the parity of individuals in a branching process. J. Appl. Prob. 13, 219–230.CrossRefGoogle Scholar