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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230683A 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.Probability60F10Martin boundary of a killed random walk on a half-spacetext