Martin boundary of a killed random walk on a quadrant

Details Martin boundary of a killed random walk on a quadrant Martin boundary of a killed random walk on a quadrant

2009-02-28

arxiv.org/abs/0903.0070v2

Annals of Probability 2010, Vol. 38, No. 3, 1106-1142

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AOP506 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/09-AOP506

A complete representation of the Martin boundary of killed random walks on the quadrant ${\mathbb{N}}^*\times{\mathbb{N}}^*$ is obtained. It is proved that the corresponding full Martin compactification of the quadrant ${\mathbb{N}}^*\times{\mathbb{N}}^*$ is homeomorphic to the closure of the set $\{w={z}/{(1+|z|)}:z\in{\mathbb{N}}^*\times{\mathbb{N}}^*\}$ in ${\mathbb{R}}^2$. The method is based on a ratio limit theorem for local processes and large deviation techniques.

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