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April, 1977 Representations of Invariant Measures on Multitype Galton-Watson Processes
Fred M. Hoppe
Ann. Probab. 5(2): 291-297 (April, 1977). DOI: 10.1214/aop/1176995854

Abstract

We show that there is a one-to-one correspondence between invariant measures for the noncritical multitype Galton-Watson process and invariant measures for the single type process with a linear offspring probability generating function. Two corollaries emerge as simple applications, the first being Spitzer's Martin boundary representation, the second giving the asymptotic behaviour of the measures. Both require no extra moment assumptions and are valid for the multitype theory.

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Fred M. Hoppe. "Representations of Invariant Measures on Multitype Galton-Watson Processes." Ann. Probab. 5 (2) 291 - 297, April, 1977. https://doi.org/10.1214/aop/1176995854

Information

Published: April, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0379.60068
MathSciNet: MR431405
Digital Object Identifier: 10.1214/aop/1176995854

Subjects:
Primary: 60J20
Secondary: 60F15

Keywords: Abel's equation , conditional Yaglom limit , Invariant measures , Martin boundary , Multitype Galton-Watson process , regular variation , Schroder's equation

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 2 • April, 1977
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