Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-06T04:19:02.896Z Has data issue: false hasContentIssue false
  • English
  • Français

An immigration super-critical branching diffusion process

Published online by Cambridge University Press:  14 July 2016

J. Radcliffe
J. Radcliffe*
Affiliation:
University of Leeds
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is an extension of Davis (1965) by allowing immigration. Mean square convergence is proved for a random variable in a branching diffusion process allowing immigration.

Keywords

IMMIGRATIONAGE DEPENDENT BRANCHINGDIFFUSIONFUNCTIONALMEAN SQUARE CONVERGENCEMIGRATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 1 , March 1972 , pp. 13 - 23
Copyright
Copyright © Applied Probability Trust 1972 

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

Bailey, N. T. J. (1968) Stochastic birth, death and migration processes for spatially distributed populations. Biometrika 55, 189–198.CrossRefGoogle Scholar
Bartlett, M. S. (1966) An Introduction to Stochastic Processes. Cambridge Univ. Press, London and New York.Google Scholar
Crump, K. S. (1970) Migratory populations in branching processes. J. Appl. Prob. 7, 565–572.CrossRefGoogle Scholar
Davis, A. W. (1965) On the theory of birth, death and diffusion processes. J. Appl. Prob. 2, 293–322.CrossRefGoogle Scholar
Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Kingman, J. F. C. (1969) Markov population processes. J. Appl. Prob. 6, 1–18.CrossRefGoogle Scholar
Moyal, J. E. (1962) The general theory of stochastic population processes. Acta Math. 108, 1–31.CrossRefGoogle Scholar
Radcliffe, J. and Staff, P. J. (1970) Immigration-migration-death processes with multiple latent roots. Math. Biosciences 8, 279–290.CrossRefGoogle Scholar