- Volume 7, Number 4 (2001), 593-604.
Martingale convergence and the functional equation in the multi-type branching random walk
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.
Bernoulli, Volume 7, Number 4 (2001), 593-604.
First available in Project Euclid: 17 March 2004
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Kyprianou, Andreas E.; Rahimzadeh Sani, A. Martingale convergence and the functional equation in the multi-type branching random walk. Bernoulli 7 (2001), no. 4, 593--604. https://projecteuclid.org/euclid.bj/1079559464