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Stationary measures for multitype branching processes

Published online by Cambridge University Press:  14 July 2016

Fred Hoppe
Fred Hoppe*
Affiliation:
Princeton University
*
*Now at the University of Alberta.
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Abstract

The multitype Galton-Watson process is considered both with and without immigration. Proofs are given for the existence of invariant measures and their uniqueness is examined by functional equation methods. Theorem 2.1 proves the uniqueness, under certain conditions, of solutions of a multidimensional Schröder equation. Regular variation is shown to play a role in the multitype theory.

Keywords

MULTITYPE BRANCHING PROCESSESIMMIGRATIONINVARIANT MEASURESFUNCTIONAL EQUATIONSREGULAR VARIATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 2 , June 1975 , pp. 219 - 227
Copyright
Copyright © Applied Probability Trust 1975 

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Footnotes

Research supported partially by the Office of Naval Research Contract N00014–670151-0017 to the Department of Statistics, Princeton University, Princeton, N. J., and by a National Research Council of Canada Postgraduate Scholarship in the Program in Applied Mathematics at Princeton University.

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