  The following question is addressed: under what conditions can a strange
diffusive process, defined by a semi-dynamical V-Langevin equation or its
associated Hybrid kinetic equation (HKE), be described by an equivalent purely
stochastic process, defined by a Continuous Time Random Walk (CTRW) or by a
Fractional Differential Equation (FDE)? More specifically, does there exist a
class of V-Langevin equations with long-range (algebraic) velocity temporal
correlation, that leads to a time-fractional superdiffusive process? The answer
is always affirmative in one dimension. It is always negative in two
dimensions: any algebraically decaying temporal velocity correlation (with a
Gaussian spatial correlation) produces a normal diffusive process. General
conditions relating the diffusive nature of the process to the temporal
exponent of the Lagrangian velocity correlation (in Corrsin approximation) are
derived.
