  We derive a hierarchy of evolution equations for multi-point probability
density functions in magneto-hydrodynamic (MHD) turbulence. We discuss the
relation to the moment hierarchy in MHD turbulence derived by Chandrasekhar and
derive a functional equation for a joint characteristic functional which can be
considered as the analogon to the Hopf functional in hydrodynamic turbulence.
Furthermore, we develop a closure method for the evolution equation of the
single-point magnetic field probability density function which is based on a
joint Gaussian assumption for unclosed terms. It is explicitly shown that this
closure, together with the assumptions of homogeneity and isotropy, leads to
vanishing nonlinear terms. We discuss the implications of this finding for
magnetic field generation and give a brief outlook on an axisymmetric theory
which includes a mean magnetic field.
