The Concept of "Strong Anomalous Diffusion"

$$ \operatorname{E}|\xi_{t}-\operatorname{E}\xi_{t}|^{q}\propto t^{q\,\nu(q)} $$ In Castiglione et al (1999) we inquired the mechanisms underlying genuine multiscaling in diffusion processes. Strong anomalous diffusion appears in fine-tuned parametric regions of chaotic dynamical systems.
In such regions the interplay between self-similar bulk behavior of the statistics and ballistic transport for the rare excursions occasions non-linear corrections \( \nu(q) \) (typically "bifractal") to the diffusion scaling exponents. A grand theoretical challenge is the developmemt of an analytical theory to compute anomalous scaling exponents. This task can be accomplished only in special cases .