Martingale convergence and the functional equation in the multi-type branching random walk

Andreas E Kyprianou, A Rahimzadeh Sani

Research output: Contribution to journalArticle

11 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)593-604
Number of pages12
JournalBernoulli
Volume7
Issue number4
Publication statusPublished - 2001

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