  The Markovian diffusion theory is generalized within the framework of the
special theory of relativity using a modification of the mathematical calculus
of diffusion on Riemannian manifolds (with definite metric) to describe
diffusion on Lorentzian manifolds with an indefinite metric. A generalized
Langevin equation in the fiber space of position, velocity and orthonormal
velocity frames is defined from which the generalized relativistic Kramers
equation in the phase space in external force fields is derived. The obtained
diffusion equation is invariant under Lorentz transformations and its
stationary solution is given by the J\"{u}ttner distribution. Besides a
non-stationary analytical solution is derived for the example of force-free
relativistic diffusion.
