A note on the Green's function for the transient random walk without   killing on the half lattice, orthant and strip
  In this note we derive an exact formula for the Green's function of the random walk on different subspaces of the discrete lattice (orthants, including the half space, and the strip) without killing on the boundary in terms of the Green's function of the simple random walk on $\mathbb{Z}^d$, $d\ge 3$. 
Alberto Chiarini and Alessandra Cipriani
math.PR