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

Abstract

A generalization of Biggins Martingale Convergence Theorem is proved for the multitype branching random walk The proof appeals to modern techniques involving the construction of sizebiased measures on the space of marked trees generated by the branching process As a simple conse quence we obtain existence and uniqueness of solutions within a specied class to a system of functional equations