  In this paper, we establish a set of criteria which are applied to discuss
various formulations under which Lagrangian stochastic models can be found.
These models are used for the simulation of fluid particles in single-phase
turbulence as well as for the fluid seen by discrete particles in dispersed
turbulent two-phase flows. A central issue is to put forward reliable
requirements which must be met by Lagrangian stochastic models and a new
element brought by the present analysis is to address the single- and two-phase
flow situations from a unified point of view.This analysis does not address the
question of the relative predictive capacities of different models but
concentrates on their formulation since advantages and disadvantages of
different formulations are not always clear. Indeed, hidden in the changes from
one structure to another are some possible pitfalls which can lead to flaws in
the construction of practical models and to physically-unsound numerical
calculations. A first interest of the present approach is illustrated by
considering some models proposed in the literature and by showing that these
criteria help to assess whether these Lagrangian stochastic models can be
regarded as acceptable descriptions. A second interest is to indicate how
future developments can be safely built, which is also relevant for stochastic
subgrid models for particle-laden flows in the context of Large Eddy
Simulations.
