Escape time for a random walk from an orthant

Let {([xi]k, [eta]k), k>[greater-or-equal, slanted]} be a sequence of independent random vectors with values in {-1, 0, ...} x{-1, 0, ...}. Assume the component variables have zero means, bounded second moments, and that [alpha] = E[[xi]k[eta]k] is the same for all k. Let Zn denote (i0,j0)+[Sigma]n1 ([xi]k, where i0, j0 are positive integers, and let [tau] denote the first time Zn hits a coordinate axis. We show E([tau]) is finite if and only if [alpha]random walk martingales stopping times