Hostname: page-component-84b7d79bbc-fnpn6 Total loading time: 0 Render date: 2024-07-30T23:55:26.660Z Has data issue: false hasContentIssue false
  • English
  • Français

Multidimensional age-dependent branching processes allowing immigration: The limiting distribution

Published online by Cambridge University Press:  14 July 2016

Norman Kaplan
Norman Kaplan*
Affiliation:
University of California, Berkeley
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper continues the author's study of age-dependent branching processes allowing immigration. In this paper the multidimensional case is considered. A sufficient condition is obtained for the existence of a legitimate limiting distribution. Several corollaries are obtained, which generalize many of the results of the discrete theory and those of the one-dimensional continuous time model.

Keywords

MULTITYPE BRANCHING PROCESSES WITH IMMIGRATIONRENEWAL THEOREMLIMITING DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 2 , June 1974 , pp. 225 - 236
Copyright
Copyright © Applied Probability Trust 1974 

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] Athreya, K. B. and Ney, P. (1972) Branching Processes. Springer, Berlin-Gottingen-Heidelberg.CrossRefGoogle Scholar
[2] Feller, W. (1966) An Introduction to Probability Theory and its Applications. Vol. 2. Wiley, New York.Google Scholar
[3] Goldstein, M. J. (1971) Critical age-dependent branching processes: Single and multitype. Z. Wahrscheinlichkeitsth. 17, 74–88.CrossRefGoogle Scholar
[4] Heathcote, C. R. (1965) Corrections and comments on the paper “A branching process involving immigration”. J. R. Statist. Soc. B 27, 213–217.Google Scholar
[5] Jagers, P. (1968) Age-dependent branching processes allowing immigration. Theor. Probability Appl. 13, 225–236.CrossRefGoogle Scholar
[6] Kaplan, N. L. (1973) Multitype Galton Watson process with immigration. Ann. of Probability. 1, 947–953.CrossRefGoogle Scholar
[7] Kaplan, N. L. and Pakes, A. G. (1974) Supercritical age-dependent branching processes allowing immigration. Submitted to Stochastic Proc. Appl. CrossRefGoogle Scholar
[8] Karlin, S. (1969) A First Course in Stochastic Processes. Academic Press, New York.Google Scholar
[9] Katz, M. (1963) The probability in the tail of a distribution. Ann. Math. Statist. 34, 312–318.CrossRefGoogle Scholar
[10] Mode, C. J. (1968) A multidimensional age-dependent branching process with applica lions to natural selection I. Math. Biosci. 3, 1–18.CrossRefGoogle Scholar
[11] Quine, M. P. (1970) The multitype Galton-Watson process with immigration. J. Appl. Prob. 7, 411–422.CrossRefGoogle Scholar
[12] Ryan, T. A. (1968) On age-dependent branching processes. Ph. D. dissertation, Cornell University.Google Scholar
[13] Pakes, A. G. and Kaplan, N. L. (1974) On the subcritical Bellman-Harris process with immigration. J. Appl. Prob. 11, No. 4. To appear.CrossRefGoogle Scholar