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

Irina Ignatiouk-Robert ()
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Irina Ignatiouk-Robert: Université de Cergy-Pontoise

Journal of Theoretical Probability, 2008, vol. 21, issue 1, 35-68

Abstract: 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 $\mathcal{S}^{d}_{+}=\{z\in \mathbb{R}^{d-1}\times\mathbb{R}_{+}: {|z|=1}\}$ . The method is based on a combination of ratio limits theorems and large deviation techniques.

Keywords: Martin boundary; Sample path large deviations; Random walk (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10959-007-0100-3

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