### Abstract

Original language | English |
---|---|

Pages (from-to) | 593-604 |

Number of pages | 12 |

Journal | Bernoulli |

Volume | 7 |

Issue number | 4 |

Publication status | Published - 2001 |

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### Cite this

*Bernoulli*,

*7*(4), 593-604.

**Martingale convergence and the functional equation in the multi-type branching random walk.** / Kyprianou, Andreas E; Rahimzadeh Sani, A.

Research output: Contribution to journal › Article

*Bernoulli*, vol. 7, no. 4, pp. 593-604.

}

TY - JOUR

T1 - Martingale convergence and the functional equation in the multi-type branching random walk

AU - Kyprianou, Andreas E

AU - Rahimzadeh Sani, A

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

M3 - Article

VL - 7

SP - 593

EP - 604

JO - Bernoulli

JF - Bernoulli

SN - 1350-7265

IS - 4

ER -