Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-29T10:33:11.362Z Has data issue: false hasContentIssue false
  • English
  • Français

The asymptotic frequencies of the types in a multitype age-dependent branching process allowing immigration

Published online by Cambridge University Press:  14 July 2016

J. Radcliffe
J. Radcliffe*
Affiliation:
Queen Mary College, London
Get access Rights & Permissions [Opens in a new window]

Abstract

The mean square and almost sure convergence of W(t) = e–αtZ(t) is proved for a super-critical multitype age-dependent branching process allowing immigration at the epochs of a renewal process. It is shown that the Malthusian parameter, asymptotic frequencies of types and stationary age distributions are the same for the processes with and without immigration.

Keywords

MULTITYPE AGE-DEPENDENT BRANCHING PROCESSIMMIGRATIONASYMPTOTIC FREQUENCIES OF TYPESMEAN SQUARE AND ALMOST SURE CONVERGENCE
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 3 , September 1973 , pp. 652 - 658
Copyright
Copyright © Applied Probability Trust 1973 

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

Harris, T. E. (1963) The Theory of Branching Processes. Springer Verlag, Berlin.10.1007/978-3-642-51866-9Google Scholar
JAGERS, P. (1968) Age-dependent branching processes allowing immigration. Teor. Veroyat. Primen. 13, 230–242. Correction ibid. 13 (1968) (Letters to Ed.)Google Scholar
Mode, C. J. (1971) Multitype Branching Processes: Theory and Applications. American Elsevier, New York.Google Scholar
Radcliffe, J. (1972a) The convergence of a generalized multitype age-dependent branching process with Poisson immigration. Math. Biosciences 13, 125–132.10.1016/0025-5564(72)90028-4Google Scholar
Radcliffe, J. (1972b) The convergence of a super-critical age-dependent branching process allowing immigration at the epochs of a renewal process. Math. Biosciences 14, 37–44.10.1016/0025-5564(72)90005-3Google Scholar