  We solve the problem of formulating Brownian motion in a relativistically
covariant framework in 1+1 and 3+1 dimensions. We obtain covariant
Fokker-Planck equations with (for the isotropic case) a differential operator
of invariant d'Alembert form. Treating the spacelike and timelike fluctuations
separately, we show that it is essential to take into account the analytic
continuation of "unphysical" fluctuations in order to achieve these results.
