  We prove the existence of a solution to an equation governing the number
density within a compact domain of a discrete particle system for a prescribed
class of particle interactions taking into account the effects of the diffusion
and drift of the set of particles. Each particle carries a number of internal
coordinates which may evolve continuously in time, determined by what we will
refer to as the internal drift, or discretely via the interaction kernels.
Perfectly reflecting boundary conditions are imposed on the system and all the
processes may be spatially and temporally inhomogeneous. We use a relative
compactness argument to construct a sequence of measures that converge weakly
to a solution of the governing equation. Since the proof of existence is a
constructive one, it provides a stochastic approximation scheme that can be
used for the numerical study of molecular dynamics.
