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.
Publié le : 2010-05-15
Classification:
Martin boundary,
sample path large deviations,
random walk,
60F10,
60J15,
60K35
@article{1275486189,
author = {Ignatiouk-Robert, Irina and Loree, Christophe},
title = {Martin boundary of a killed random walk on a quadrant},
journal = {Ann. Probab.},
volume = {38},
number = {1},
year = {2010},
pages = { 1106-1142},
language = {en},
url = {http://dml.mathdoc.fr/item/1275486189}
}
Ignatiouk-Robert, Irina; Loree, Christophe. Martin boundary of a killed random walk on a quadrant. Ann. Probab., Tome 38 (2010) no. 1, pp. 1106-1142. http://gdmltest.u-ga.fr/item/1275486189/