Anomalous spreading and misidentification of spatial random walk models

Anomalous diffusive spreading behaviors are often modeled with continuous-time random walks or fractional Brownian motion, while spatial directional preference is the key attribute of correlated random walks. In this paper, we construct and analyze a spatial random walk model with particular attention to the synthesis of anomalous diffusive behaviors and spatial directional preference, as well as statistical inference under discrete sampling. Anisotropic anomalous diffusive behaviors of the proposed model emerge from the long memory among step lengths, standing in contrast to little tangling diffusive trajectories of correlated random walk models, designed directly through the relative turning angles. With the help of the proposed model, we demonstrate difficulty in model identification among spatial random walk models and suggest that the identification procedure be planned and carried out with a great deal of caution.