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

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.

13 pages, 1 figure

References in corpus (3)

• Large deviations for processes with discontinuous statistics
• Martin boundary of a reflected random walk on a half-space
• Random Walks in the Quarter Plane Absorbed at the Boundary : Exact and Asymptotic

Cited by in corpus (3)

• Asymptotic behavior of the occupancy density for obliquely reflected Brownian motion in a half-plane and Martin boundary
• $t$-Martin boundary of killed random walks in the quadrant
• Martin boundary of a space-time Brownian motion with drift killed at the boundary of a moving cone