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A note on the multitype measure branching process

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Zeng-Hu Li
Zeng-Hu Li*
Affiliation:
Beijing Normal University
*
∗ Postal address: Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China.
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Abstract

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The existence of a class of multitype measure branching processes is deduced from a single-type model introduced by Li [8], which extends the work of Gorostiza and Lopez-Mimbela [5] and shows that the study of a multitype process can sometimes be reduced to that of a single-type one.

Keywords

SINGLE-TYPESUPERPROCESSHOMEOMORPHISM

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60G57: Random measures
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 24 , Issue 2 , June 1992 , pp. 496 - 498
Copyright
Copyright © Applied Probability Trust 1992 

Footnotes

Research supported in part by the National Natural Science Foundation of China.

References

[1] Athreya, K. B. and Ney, P. E. (1972) Branching Processes. Springer-Verlag, Berlin.Google Scholar
[2] Dynkin, E. B. (1965) Markov Processes, Vol. 1, Springer-Verlag, Berlin.Google Scholar
[3] Dynkin, E. B. (1991) Branching particle systems and superprocesses. Ann. Prob. 19, 1157–1194.Google Scholar
[4] Getoor, R. K. (1975) Markov Processes: Ray Processes and Right Processes. Lecture Notes in Mathematics 440, Springer-Verlag, Berlin.Google Scholar
[5] Gorostiza, L. G. and Lopez-Mimbela, J. A. (1990) The multitype branching process. Adv. Appl. Prob. 22, 49–67.Google Scholar
[6] Li, Z. H. (1991) Integral representations of continuous functions. Chinese Sci. Bull. 36, 979–983.Google Scholar
[7] Li, Z. H. (1990) Measure-valued branching processes with immigration. Stoch. Proc. Appl. To appear.Google Scholar
[8] Li, Z. H. (1990) Branching particle systems with immigration. Second Sino-French Mathematics Meeting, Sep. 24-Oct. 11, Lecture Notes in Mathematics, Springer-Verlag, Berlin. To appear.Google Scholar