Martin boundary of a killed random walk on a half-space

Details Martin boundary of a killed random walk on a half-space Martin boundary of a killed random walk on a half-space

2006-06-19

arxiv.org/abs/math/0606439v2

Journal of Theoretical Probability, 2008, V 21, n 1, pp 35-68

Mathematics

Probability

Scientific paper

A complete representation of the Martin boundary of killed random walks on a
half-space $\Z^{d-1}\times\N^*$ is obtained. In particular, it is proved that
the corresponding Martin boundary is homemorphic to the half-sphere ${\cal
S}^d_+ = \{z\in\R^{d-1}\times\R_+ : |z|=1\}$. The method is based on a
combination of ratio limits theorems and large deviation techniques.

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