  Extending the statistical approach proposed in a parallel paper \cite%
{Tessarotto2008-aa}, purpose of this work is to propose a stochastic inverse
kinetic theory for small-scale hydrodynamic turbulence based on the
introduction of a suitable \textit{local phase-space probability density
function} (pdf). In particular, we pose the problem of the construction of
Fokker-Planck kinetic models of hydrodynamic turbulence. The approach here
adopted is based on the so-called IKT approach (inverse kinetic theory),
developed by Ellero et al. (2004-2008) which permits an exact phase-space
description of incompressible fluids based on the adoption of a local pdf. We
intend to show that for prescribed models of stochasticity the present approach
permits to determine uniquely the time evolution of the stochastic fluid
fields. The stochastic-averaged local pdf is shown to obey a kinetic equation
which, although generally non-Markovian, locally in velocity-space can be
approximated by means of a suitable Fokker-planck kinetic equation. As a side
result, the same pdf is proven to have generally a non-Gaussian behavior.
