Simple model of a random walk with arbitrarily long memory - art. no. 031109

We present a generalization of the persistent random-walk model in which th e step at time n depends on the stare of the step at time n-T, for arbitrar y T. This gives rise to arbitrarily long memory effects, yet by an appropri ate transformation the model is tractable by essentially the same technique s applicable to the usual persistent random-walk problem. We apply our resu lts to the specific case of delayed "step'' persistence, and analyze its as ymptotic statistical properties.