On Seneta-Heyde Scaling for a stable branching random walk

We consider a discrete-time branching random walk in the boundary case, where the associated random walk is in the domain of attraction of an alpha-stable law with 1 < alpha < 2. We prove that the derivative martingale D-n converges to a nontrivial limit D-infinity under some regular conditions. We also study the additive martingale W-n and prove that n(1/alpha) W-n converges in probability to a constant multiple of D-infinity.