Martin boundary of a killed random walk on a quadrant

Abstract

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

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

References in corpus (3)

• Bridges and networks: Exact asymptotics
• Martin boundary of a reflected random walk on a half-space
• Random Walks in the Quarter Plane Absorbed at the Boundary : Exact and Asymptotic

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