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 language | English |
|---|---|
| Pages (from-to) | 593-604 |
| Number of pages | 12 |
| Journal | Bernoulli |
| Volume | 7 |
| Issue number | 4 |
| Publication status | Published - 2001 |