  Turbulence at kinetic scales is an unresolved and ubiquitous phenomenon that
characterizes both space and laboratory plasmas. Recently, new theories, {\it
in-situ} spacecraft observations and numerical simulations suggest a novel
scenario for turbulence, characterized by a so-called phase space cascade --
the formation of fine structures, both in physical and velocity space. This new
concept is here extended by directly taking into account the role of
inter-particle collisions, modeled through the nonlinear Landau operator or the
simplified Dougherty operator. The characteristic times, associated with
inter-particle correlations, are derived in the above cases. The implications
of introducing collisions on the phase space cascade are finally discussed.
