  We provide a quantum field theoretical derivation of the
Abraham-Lorentz-Dirac (ALD) equation, describing the motion of an electric
point charge sourcing an electromagnetic field, which back-reacts on the charge
as a self-force, and the Mino-Sasaki-Tanaka-Quinn-Wald (MSTQW) equation
describing the motion of a point mass with self-force interacting with the
linearized metric perturbations caused by the mass off an otherwise vacuous
curved background spacetime. We regularize the formally divergent self-force by
smearing the direct part of the retarded Green's function and using a
quasilocal expansion. We also derive the ALD-Langevin and the MSTQW-Langevin
equations with a classical stochastic force accounting for the effect of the
quantum fluctuations in the field, which causes small fluctuations on the
particle trajectory. These equations will be useful for studying the stochastic
motion of charges and small masses under the influence of both quantum and
classical noise sources, derived either self-consistently or put in by hand
phenomenologically. We also show that history-dependent noise-induced drift
motions could arise from such stochastic sources on the trajectory that could
be a hidden feature of gravitational wave forms hitherto unknown.
