Abstract
Let be a mean zero -stable random walk on with inhomogeneous jump rates , with and a family of independent random variables with common marginal distribution in the basin of attraction of an -stable law, . In this paper, we derive results about the long-time behavior of this process, in particular its scaling limit, given by a -stable process time changed by the inverse of another process, involving the local time of the -stable process and an independent -stable subordinator; we call the resulting process a quasistable process. Another such result concerns aging. We obtain an (integrated) aging result for chi.