Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T15:42:43.663Z Has data issue: false hasContentIssue false
  • English
  • Français

General branching processes with immigration

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Peter Olofsson
Peter Olofsson*
Affiliation:
Chalmers University of Technology
*
∗Postal address: Department of Mathematics, Chalmers University of Technology, Göteborg, Sweden.
Get access Rights & Permissions [Opens in a new window]

Abstract

A general multi-type branching process where new individuals immigrate according to some point process is considered. An intrinsic submartingale is defined and a convergence result for processes counted with random characteristics is obtained. Some examples are given.

Keywords

GENERAL BRANCHING PROCESSMULTI-TYPEIMMIGRATION

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 4 , December 1996 , pp. 940 - 948
Copyright
Copyright © Applied Probability Trust 1996 

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

Asmussen, S. and Hering, H. (1976) Strong limit theorems for supercritical immigration-branching processes. Math. Scand. 39, 327–342.Google Scholar
Asmussen, S. and Hering, H. (1983) Branching Processes. Birkhäuser, Boston.Google Scholar
Durrett, R. (1991) Probability: Theory and Examples. Wadsworth, Pacific Grove, CA.Google Scholar
Jagers, P. (1975) Branching Processes with Biological Applications. Wiley, Chichester.Google Scholar
Jagers, P. (1989) General branching processes as Markov fields. Stoch. Proc. Appl. 32, 183–212.Google Scholar
Jagers, P. (1992) Stabilities and instabilities in population dynamics. J. Appl. Prob. 29, 770–780.Google Scholar
Lyons, R., Pemantle, R. and Peres, Y. (1995) Conceptual proofs of L log L criteria for mean behaviour of branching processes. Ann. Prob. 3, 1125–1138.Google Scholar
Nerman, O. (1981) On the convergence of supercritical general (C-M-J) branching processes. Z. Wahrscheinlichkeitsth. 57, 365–395.Google Scholar
Seneta, E. (1970) On the supercritical branching process with immigration. Math. Biosci. 7, 9–14.CrossRefGoogle Scholar
Shurenkov, V. M. (1992) Markov renewal theory and its applications to Markov ergodic processes. Preprint. Department of Mathematics, Chalmers University of Technology and Göteborg University.Google Scholar