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August 2001 Martingale convergence and the functional equation in the multi-type branching random walk
Andreas E. Kyprianou, A. Rahimzadeh Sani
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Bernoulli 7(4): 593-604 (August 2001).

Abstract

A generalization of Biggins's martingale convergence theorem is proved for the multi-type branching random walk. The proof appeals to modern techniques involving the construction of size-biased measures on the space of marked trees generated by the branching process. As a simple consequence we obtain existence and uniqueness of solutions (within a specified class) to a system of functional equations.

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Andreas E. Kyprianou. A. Rahimzadeh Sani. "Martingale convergence and the functional equation in the multi-type branching random walk." Bernoulli 7 (4) 593 - 604, August 2001.

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Published: August 2001
First available in Project Euclid: 17 March 2004

zbMATH: 1017.60090
MathSciNet: MR2002G:60069

Keywords: functional equation , multi-type branching random walk , size-biased measures

Rights: Copyright © 2001 Bernoulli Society for Mathematical Statistics and Probability

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Vol.7 • No. 4 • August 2001
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