Martin boundary of a killed random walk on a quadrant
type: Item
instance of: scholarly article
title: Martin boundary of a killed random walk on a quadrant
zbMATH Open document ID: 1205.60057
DOI: 10.1214/09-AOP506
author: Irina Ignatiouk-Robert
author: Christophe Loree
published in: The Annals of Probability
publication date: 2010-07-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/0903.0070
review text: The authors derive a complete representation of the Martin boundary of killed random walks on the quadrant \(\mathbb{N}^{\ast }\times \mathbb{N}^{\ast }\). 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 \(\left\{ w=z/\left( 1+\left| z\right| \right) :z\in \mathbb{N}^{\ast }\times \mathbb{N} ^{\ast }\right\} \) in \( \mathbb{R} ^{2}\). The method is based on a ratio limit theorem for local processes and large deviation techniques.
reviewed by: Marius Iosifescu
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 5757652
zbMATH Keywords: Martin boundary
zbMATH Keywords: sample path large deviations
zbMATH Keywords: random walk
MaRDI profile type: Publication
arXiv ID: 0903.0070
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description: scientific article