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

Irina Ignatiouk-Robert

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

Irina Ignatiouk-Robert

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Abstract

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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BibTeX RIS

Irina Ignatiouk-Robert. 2007-03-14. Martin boundary of a killed random walk on a half-space. https://arxiv.org/abs/math/0606439

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