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Martin Boundary of a Killed Random Walk on a Half-Space

Authors:	Irina Ignatiouk-Robert

Affiliation:	(1) Département de mathématiques, Université de Cergy-Pontoise, 2, Avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France

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

Keywords:	Martin boundary Sample path large deviations Random walk
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