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A Limit Theorem for Discrete Galton-Watson Branching Processes with Immigration

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Zenghu Li
Zenghu Li*
Affiliation:
Beijing Normal University
*
∗ Postal address: School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China. Email address: lizh@bnu.edu.cn
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Abstract

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We provide a simple set of sufficient conditions for the weak convergence of discrete-time, discrete-state Galton-Watson branching processes with immigration to continuous-time, continuous-state branching processes with immigration.

Keywords

Markov chainbranching process with immigrationlimit theoremweak convergencegenerating function

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Short Communications
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 289 - 295
Copyright
© Applied Probability Trust 2006 

References

Ethier, S. N. and Kurtz, T. G. (1986). Markov Processes: Characterization and Convergence. John Wiley, New York.Google Scholar
Hewitt, E. and Stromberg, K. (1965). Real and Abstract Analysis. Springer, Berlin.Google Scholar
Itô, K. and McKean, H. P. Jr. (1965). Diffusion Processes and their Sample Paths. Springer, Berlin.Google Scholar
Kawazu, K. and Watanabe, S. (1971). Branching processes with immigration and related limit theorems. Theory Prob. Appl. 16, 36–54.CrossRefGoogle Scholar
Le Gall, J.-F. and Le Jan, Y. (1998). Branching processes in Lévy processes: the exploration process. Ann. Prob. 26, 213–252.Google Scholar
Li, Z. H. (1991). Integral representations of continuous functions. Chinese Sci. Bull. 36, 979–983.Google Scholar
Li, Z. H. (1992). Measure-valued branching processes with immigration. Stoch. Process. Appl. 43, 249–264.Google Scholar
Pitman, J. and Yor, M. (1982). A decomposition of Bessel bridges. Z. Wahrscheinlichkeitsth. 59, 425–457.Google Scholar
Shiga, T. and Watanabe, S. (1973). Bessel diffusions as a one-parameter family of diffusion processes. Z. Wahrscheinlichkeitsth. 27, 37–46.Google Scholar