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A note on Markov branching processes

Published online by Cambridge University Press:  01 July 2016

Fred M. Hoppe*
Affiliation:
The University of Michigan, Ann Arbor
*
Postal address: Department of Statistics, The University of Michigan, Ann Arbor, MI 48109, USA.
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Abstract

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We present a simple proof of Zolotarev’s representation for the Laplace transform of the normalized limit of a Markov branching process and relate it to the Harris representation.

Type
Letters to the Editor
Copyright
Copyright © Applied Probability Trust 1985 

References

Harris, T. E. (1951) Some mathematical models for branching processes. Proc. 2nd Berkeley Symposium on Mathematical Statistics and Probability , pp 305328.Google Scholar
Karlin, S. and Mcgregor, J. (1968) Embeddability of discrete time simple branching processes into continuous time branching processes. Trans. Amer. Math. Soc. 132, 115136.Google Scholar
Seneta, E. (1968) On recent theorems concerning the supercritical Galton-Watson process. Ann. Math. Statist. 39, 20982102.CrossRefGoogle Scholar
Seneta, E. (1969) Functional equations and the Galton-Watson process. Adv. Appl. Prob. 1, 142.Google Scholar
Zolotarev, V. M. (1957) More exact statements of several theorems in the theory of branching processes. Theory Prob. Appl. 2, 245253.CrossRefGoogle Scholar