Martin boundary of a killed non-centered random walk in a general cone

Irina Ignatiouk-Robert

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arXiv · 2006.15870

Martin boundary of a killed non-centered random walk in a general cone

Irina Ignatiouk-Robert

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Abstract

We investigate Martin boundary for a non-centered random walk on ${\mathbb Z}^d$ killed up on the time $τ_\vartheta$ of the first exit from a convex cone with a vertex at $0$. The approach combines large deviation estimates, the ratio limite theorem and the ladder height process. The results are applied to identify the Martin boundary for a random walk killed upon the first exit from a convex cone having $C^1$ boundary.

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Irina Ignatiouk-Robert. 2020-06-29. Martin boundary of a killed non-centered random walk in a general cone. https://arxiv.org/abs/2006.15870

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