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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

Information

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

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