Kyprianou, Andreas E.; Rahimzadeh Sani, A. Martingale convergence and the functional equation in the multi-type branching random walk. (English) Zbl 1017.60090 Bernoulli 7, No. 4, 593-604 (2001). The authors prove a generalization of Biggins’s martingale convergence theorem for the multi-type branching random walk by constructing size-biased measures on the space of marked trees generated by the branching process. Existence and uniqueness of solutions for a system of functional equations are then obtained. Reviewer: Mihai Gradinaru (Nancy) Cited in 7 Documents MSC: 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 60G50 Sums of independent random variables; random walks 60F15 Strong limit theorems Keywords:multitype branching random walk; size-biased measures; functional equation; martingale convergence PDFBibTeX XMLCite \textit{A. E. Kyprianou} and \textit{A. Rahimzadeh Sani}, Bernoulli 7, No. 4, 593--604 (2001; Zbl 1017.60090) Full Text: DOI Link