The t-Martin boundary of reflected random walks on a half-space

TL;DR

This paper characterizes the t-Martin boundary for reflected random walks on a half-space, revealing that these boundaries vary with t and are not topologically equivalent across different t values.

Contribution

It identifies the t-Martin boundary for reflected random walks on a half-space and demonstrates its instability across different t values.

Findings

The t-Martin boundary is explicitly identified.

The t-Martin boundary varies with t and is not homeomorphic for different t.

The boundary's structure depends on the reflection conditions.

Abstract

The t-Martin boundary of a random walk on a half-space with reflected boundary conditions is identified. It is shown in particular that the t-Martin boundary of such a random walk is not stable in the following sense : for different values of t, the t-Martin compactifications are not homeomorphic to each other.