Local asymptotics for the time of first return to the origin of   transient random walk
  We consider a transient random walk on $Z^d$ which is asymptotically stable, without centering, in a sense which allows different norming for each component. The paper is devoted to the asymptotics of the probability of the first return to the origin of such a random walk at time $n$. 
Ron Doney, Dmitry Korshunov
math.PR