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

Probability Density Functions in Homogeneous and Isotropic Magneto-Hydrodynamic Turbulence