  Density dependent families of Markov chains, such as the stochastic models of
mass-action chemical kinetics, converge for large values of the indexing
parameter $N$ to deterministic systems of differential equations (Kurtz, 1970).
Moreover for moderate $N$ they can be strongly approximated by paths of a
diffusion process (Kurtz, 1976). Such an approximation however fails if the
state space is bounded (at zero or at a constant maximum level due to
conservation of mass) and if the process visits the boundaries with non
negligible probability. We present a strong approximation by a jump-diffusion
process which is robust to this event. The result is illustrated with a
particularly hard case study.
