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A multi-type critical age-dependent branching process with immigration

Published online by Cambridge University Press:  14 July 2016

Howard J. Weiner
Howard J. Weiner*
Affiliation:
University of California, Davis
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Abstract

In a multi-type critical age-dependent branching process with immigration, the numbers of cell types alive at time t, each divided by t, as t becomes large, tends to a one-dimensional gamma distribution law. The method of proof employs generating functions and compution of asymptotic moments. Connections with earlier results and extensions are indicated.

Keywords

MULTI-TYPE CRITICAL AGE-DEPENDENT BRANCHINGIMMIGRATIONGAMMA LIMIT LAW
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 4 , December 1972 , pp. 697 - 706
Copyright
Copyright © Applied Probability Trust 1972 

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References

[1] Durham, S. (1971) Limit theorems for a general critical branching process. J. Appl. Prob. 8, 1–16.Google Scholar
[2] Fildes, R. (1971) The age-dependent branching process with variable lifetime distribution. Ph.D. Thesis , University of California, Davis.Google Scholar
[3] Foster, J. H. (1969) Branching processes involving immigration. Ph.D. Thesis, University of Wisconsin.Google Scholar
[4] Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin (American edition, Prentice Hall, New York).Google Scholar
[5] Jagers, P. (1968) Age-dependent branching processes allowing immigration. Theor. Probability Appl. 13, 225–236.Google Scholar
[6] Karlin, S. (1966) A First Course in Stochastic Processes. Academic Press, New York.Google Scholar
[7] Mode, C. J. (1971) Multi-type Branching Processes—Theory and Applications. American-Elsevier, New York.Google Scholar
[8] Weiner, H. J. (1965) Asymptotic properties of an age-dependent branching process. Ann. Math. Statist. 36, 1565–1568.Google Scholar
[9] Weiner, H. J. (1970) On a multi-type critical age-dependent branching process. J. Appl. Prob. 7, 523–543.Google Scholar
[10] Weiner, H. J. (1972) Critical age-dependent branching processes. Sixth Berkeley Symposium on Probability and Statistics—Health Sciences Volume. University of California Press, Berkeley and Los Angeles. To appear.Google Scholar
[11] Weiner, H. J. (Submitted) A critical age-dependent branching process with immigration.Google Scholar
[12] Widder, D. V. (1946) The Laplace Transform. Princeton University Press, Princeton, New Jersey.Google Scholar