Necessary criterion for distinguishing true superdiffusion from correlated random walk processes

A difficulty in interpreting phenomena related to anomalous diffusion concerns how to identify scale invariant superdiffusive from Markovian correlated random walk processes. Here we propose a criterion that can distinguish between these two kinds of random walks and describe its usefulness in interpreting real data. To do so, we estimate the correlation time tau of the orientation persistence of a general correlated random walk. If the experimentally observed random walk appears diffusive on scales larger than tau, then the data cannot support the possibility of superdiffusion. We argue that the criterion is a necessary but not sufficient condition for establishing true superdiffusive behavior.