Are Lagrangian stochastic models at odds with statistical theories of relative dispersion?

In an article on statistical modelling of turbulent relative dispersion, Franzese & Cassiani (2007, p. 402) commented on Lagrangian stochastic models and reported some concern about the consistency between statisti- cal and stochastic modelling of turbulent dispersion. In this short article, comparison of the two approaches is performed. As far as the dependence of models from turbulence constants is concerned, the two theoretical ap- proaches are found to be in perfect agreement eliminating every possible concern.