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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Martingale Convergence Theorem
Branching Random Walk
Multitype
Appeal
Branching process
Existence and Uniqueness of Solutions
Martingale
Functional equation
Biased
Class
Generalization

Cite this

Martingale convergence and the functional equation in the multi-type branching random walk. / Kyprianou, Andreas E; Rahimzadeh Sani, A.

In: Bernoulli, Vol. 7, No. 4, 2001, p. 593-604.

Research output: Contribution to journalArticle

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