  We discuss a relativistic diffusion in the proper time in an approach of
Schay and Dudley. We derive (Langevin) stochastic differential equations in
various coordinates.We show that in some coordinates the stochastic
differential equations become linear. We obtain momentum probability
distribution in an explicit form.We discuss a relativistic particle diffusing
in an external electromagnetic field. We solve the Langevin equations in the
case of parallel electric and magnetic fields. We derive a kinetic equation for
the evolution of the probability distribution.We discuss drag terms leading to
an equilibrium distribution.The relativistic analog of the Ornstein-Uhlenbeck
process is not unique. We show that if the drag comes from a diffusion
approximation to the master equation then its form is strongly restricted. The
drag leading to the Tsallis equilibrium distribution satisfies this restriction
whereas the one of the Juettner distribution does not. We show that any
function of the relativistic energy can be the equilibrium distribution for a
particle in a static electric field. A preliminary study of the time evolution
with friction is presented. It is shown that the problem is equivalent to
quantum mechanics of a particle moving on a hyperboloid with a potential
determined by the drag. A relation to diffusions appearing in heavy ion
collisions is briefly discussed.
