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 " un...
