  A theory for (1+3)-dimensional relativistic Brownian motion under the
influence of external force fields is put forward. Starting out from a set of
relativistically covariant, but multiplicative Langevin equations we describe
the relativistic stochastic dynamics of a forced Brownian particle. The
corresponding Fokker-Planck equations are studied in the laboratory frame
coordinates. In particular, the stochastic integration prescription, i.e. the
discretization rule dilemma, is elucidated (pre-point discretization rule {\it
vs.} mid-point discretization rule {\it vs.} post-point discretization rule).
Remarkably, within our relativistic scheme we find that the post-point rule (or
the transport form) yields the only Fokker-Planck dynamics from which the
relativistic Maxwell-Boltzmann statistics is recovered as the stationary
solution. The relativistic velocity effects become distinctly more pronounced
by going from one to three spatial dimensions. Moreover, we present numerical
results for the asymptotic mean square displacement of a free relativistic
Brownian particle moving in (1+3) dimensions.
