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Some limit theorems for a subcritical branching process by immigration

Published online by Cambridge University Press:  14 July 2016

Y. S. Chow  and
K. F. Yu
Y. S. Chow*
Affiliation:
Columbia University
K. F. Yu*
Affiliation:
Yale University
*
∗ Postal address: Department of Mathematical Statistics, Columbia University, New York, NY 10027, U.S.A.
∗∗ Postal address: Department of Statistics, Yale University, Box 2179, Yale Station, New Haven, CT 06520–2179, U.S.A.
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Abstract

The strong law of large numbers of the Marcinkiewicz–Zygmund type is established for the total population in a subcritical branching process with immigration. The moment convergence of the total population is obtained under appropriate moment conditions on the offspring distribution and the immigration distribution.

Keywords

MARCINKIEWICZ–ZYGMUND TYPE STRONG LAW OF LARGE NUMBERSMOMENT CONVERGENCEUNIFORM INTEGRABILITYMARKOV CHAINPOSITIVE RECURRENT STATEMARTINGALE
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 1 , March 1984 , pp. 50 - 57
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

Research supported by NSF-MCS-8201723.

References

Chow, Y. S. (1971) On the Lp-convergence for n–1/p Sn, 02. Ann. Math. Statist. 42, 393–394.CrossRefGoogle Scholar
Chow, Y. S. and Teicher, H. (1978) Probability Theory. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Hall, P. (1978) The convergence of moments in the martingale central limit theorem. Z. Wahrscheinlichkeitsth. 44, 253–260.CrossRefGoogle Scholar
Heyde, C. C. and Seneta, E. (1972) Estimation theory for growth and immigration rates in a multiplicative process. J. Appl. Prob. 9, 235–256.CrossRefGoogle Scholar
Heyde, C. C. and Seneta, E. (1974) Notes on “Estimation theory for growth and immigration rates in a multiplicative process”. J. Appl. Prob. 11, 572–577.CrossRefGoogle Scholar
Pyke, R. and Root, D. (1968) On convergence in r-mean of normalized partial sums. Ann. Math. Statist. 39, 379–381.CrossRefGoogle Scholar
Quine, M. P. (1976) Asymptotic results for estimators in a subcritical branching process with immigration. Ann. Prob. 4, 319–325.CrossRefGoogle Scholar