  We address the problem of a microscopic derivation of the Langevin equation
for a weakly relativistic Brownian particle. A non-covariant Hamiltonian model
is adopted, in which the free motion of particles is described
relativistically, while their interaction is treated classically, i.e. by means
of action-to-a-distance interaction potentials. Relativistic corrections to the
classical Langevin equation emerge as nonlinear dissipation terms and originate
from the nonlinear dependence of the relativistic velocity on momentum. On the
other hand, similar nonlinear dissipation forces also appear as classical
(non-relativistic) corrections to the weak-coupling approximation. It is shown
that these classical corrections, which are usually ignored in phenomenological
models, may be of the same order of magnitude, if not larger than relativistic
ones. The interplay of relativistic corrections and classical
beyond-the-weak-coupling contributions determines the sign of the leading
nonlinear dissipation term in the Langevin equation, and thus is qualitatively
important.
