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

2020/06/29 by Irina Ignatiouk-Robert, Ignatiouk-Robert, Irina
Computer Science · Mathematics · #31C05 #60J10 #60J45 #60J50 #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2006.15870

openalex publication_date 2020/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate Martin boundary for a non-centered random walk on \mathbb Z^d killed up on the time τ_ϑ 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 C¹ boundary.

Related

• Martin boundary of random walks in convex cones
• Green function of a random walk in a cone
• Martin boundary of a killed random walk on \Z₊^d
• Boundary behavior for random walks in cones
• Stable random walks in cones