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Martingale convergence and the functional equation in the multi-type branching random walk. (English) Zbl 1017.60090

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.

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60G50 Sums of independent random variables; random walks
60F15 Strong limit theorems
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