Open Access
May 2010 Martin boundary of a killed random walk on a quadrant
Irina Ignatiouk-Robert, Christophe Loree
Ann. Probab. 38(3): 1106-1142 (May 2010). DOI: 10.1214/09-AOP506


A complete representation of the Martin boundary of killed random walks on the quadrant ℕ*×ℕ* is obtained. It is proved that the corresponding full Martin compactification of the quadrant ℕ*×ℕ* is homeomorphic to the closure of the set {w=z/(1+|z|) : z∈ℕ*×ℕ*} in ℝ2. The method is based on a ratio limit theorem for local processes and large deviation techniques.


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Irina Ignatiouk-Robert. Christophe Loree. "Martin boundary of a killed random walk on a quadrant." Ann. Probab. 38 (3) 1106 - 1142, May 2010.


Published: May 2010
First available in Project Euclid: 2 June 2010

zbMATH: 1205.60057
MathSciNet: MR2674995
Digital Object Identifier: 10.1214/09-AOP506

Primary: 60F10
Secondary: 60J15 , 60K35

Keywords: Martin boundary , Random walk , sample path large deviations

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 3 • May 2010
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