Comment on "Non-Normalizable Densities in Strong Anomalous Diffusion: Beyond the Central Limit Theorem"

A comment on the Letter by A. Rebenshtok, S. Denisov, P. H\"anggi, and E. Barkai, Phys. Rev. Lett., vol. 112, 110601 (2014). It is shown that the recent claims that the particle distributions or densities can become non-normalizable in the case of anomalous Levy walk diffusion cannot be justified. In particular, one can define a normalizable finite-time density which become infinite covariant density (ICD) in the limit of infinite time. The former one can be used to find any generalized moment, while the latter one does not. In this respect, we point out that any decent real or numerical experiment is done in finite time. Hence, ICD does not correspond to any physical reality, contrary to the claims made.