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

Strong approximation of density dependent Markov chains on bounded domains