Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-13T06:49:42.023Z Has data issue: false hasContentIssue false
  • English
  • Français

Weak convergence of the simple birth-and-death process

Published online by Cambridge University Press:  14 July 2016

Constantin Ivan
Constantin Ivan*
Affiliation:
University of Duisburg
*
∗Postal address: Gesamthochschule Duisburg, Fachbereich 11, Postfach 10 16 29, 4100 Duisburg 1, W. Germany.
Get access Rights & Permissions [Opens in a new window]

Abstract

The existence of a weak limit birth-and-death process on the natural integers for the simple birth-and-death process conditional on non-extinction up to time t as t→∞ is proved. Starting from the latter a new weak limiting procedure yields a diffusion Markov process on the positive infinite semi-axis.

Keywords

SIMPLE BIRTH-AND-DEATH PROCESSESWEAK CONVERGENCE
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 245 - 252
Copyright
Copyright © Applied Probability Trust 

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] Darroch, J. N. and Seneta, E. (1967) On quasi-stationary distributions in absorbing continuous-time finite Markov chains. J. Appl. Prob. 4, 192–196.Google Scholar
[2] Feller, W. (1966) An Introduction to Probability Theory and its Applications, Vol. II. Wiley, New York.Google Scholar
[3] Iosifescu, M. and Tautu, P. (1973) Stochastic Processes and Applications in Biology and Medicine, Vol. 1: Theory. Ed. Academiei Bucuresti; Springer-Verlag, Berlin.Google Scholar
[4] Magnus, W., Oberhettinger, F. and Soni, R. P. (1966) Formulas and Theorems for the Special Functions of Mathematical Physics. 3rd Edition. Springer, Berlin.Google Scholar
[5] Muthsam, H. (1972) Teilprozesse Markoffscher Ketten. Anz. Österreich. Akad. Wiss. Math. — Naturwiss. Kl. 4, 91–95.Google Scholar