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

Abstract

We investigate Martin boundary for a non-centered random walk on ${\mathbb{Z}}^d$ killed up on the time ${\tau }_{\vartheta }$ 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.

References in corpus (1)

• Random Walks in the Quarter Plane Absorbed at the Boundary : Exact and Asymptotic