Limit theorems for a minimal random walk model

We study the minimal random walk introduced by Kumar, Harbola and Lindenberg. It is a random process on \{0, 1, \ldots \}with unbounded memory which exhibits subdiffusive, diffusive and superdiffusive regimes. We prove the law of large numbers for the whole parameter set. Then we prove the central limit theorem and the law of the iterated logarithm for the minimal random walk under diffusive and marginally superdiffusive behaviors. More...