  We show how to find the physical Langevin equation describing the
trajectories of particles undergoing collisionless stochastic acceleration.
These stochastic differential equations retain not only one-, but two-particle
statistics, and inherit the Hamiltonian nature of the underlying microscopic
equations. This opens the door to using stochastic variational integrators to
perform simulations of stochastic interactions such as Fermi acceleration. We
illustrate the theory by applying it to two example problems.
