  Diffusion tensor coefficients play a central role in describing cosmic-ray
transport in various astrophysical environments permeated with magnetic fields,
which are usually modeled as a fluctuating field on top of a mean field. In
this article, a formal derivation of these coefficients is presented by means
of the calculation of velocity decorrelation functions of particles. It relies
mainly on expanding the 2-pt correlation function of the (fluctuating) magnetic
field experienced by the particles between two successive times in the form of
an infinite Dyson series and retaining a class of terms that converge to a
physical solution. Subsequently, the velocity decorrelation functions,
themselves expressed as Dyson series, are deduced from an iteration procedure
that improves on the partial summation scheme. The results are shown to provide
approximate solutions compared to those obtained by Monte-Carlo simulations as
long as the Larmor radius of the particles is larger than at least one tenth of
the largest scale of the turbulence.
