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November, 1982 A Limit Theorem on a Subcritical Galton-Watson Process with Immigration
K. N. Venkataraman, K. Nanthi
Ann. Probab. 10(4): 1069-1074 (November, 1982). DOI: 10.1214/aop/1176993730


For a sub-critical Galton-Watson process $\mathbf{X}$ with immigration, estimators have been studied by Pakes (1971) for the mean of the stationary distribution of $\mathbf{X}$, and by Nanthi (1979) for the offspring mean and the immigration mean of $\mathbf{X}$. These estimators have been shown by them to be asymptotically normal. In this paper it is shown that they have a joint limiting distribution which is singularly normal.


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K. N. Venkataraman. K. Nanthi. "A Limit Theorem on a Subcritical Galton-Watson Process with Immigration." Ann. Probab. 10 (4) 1069 - 1074, November, 1982.


Published: November, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0498.62073
MathSciNet: MR672309
Digital Object Identifier: 10.1214/aop/1176993730

Primary: 62M99
Secondary: 60F99

Keywords: limit distribution , Subcritical Galton-Watson process with immigration

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 4 • November, 1982
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