We prove the existence and uniqueness of a discrete nonnegative harmonic function for a
random walk satisfying finite range, centering and ellipticity conditions, killed when leaving a …

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 …

Consider a random walk {S (n), n≥ 1} on Rd, d≥ 2, where S (n)=∑ ni= 1 X (i) with {X (n),
n≥ 1} is a family of iid random variables in Rd. Let K⊂ Rd be an open cone and τx= inf {n≥ …