Relativistic diffusive motion in random electromagnetic fields

We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper time. The dynamics in the laboratory time gives the diffusive transport equation corresponding to the Juettner equilibrium at the inverse temperature \beta^{-1}=mc^{2}. The diffusion constant is expressed by the field strength correlation function (Kubo's formula).