  The aim of this article is to provide a scheme for simulating diffusion
processes evolving in one-dimensional discontinuous media. This scheme does not
rely on smoothing the coefficients that appear in the infinitesimal generator
of the diffusion processes, but uses instead an exact description of the
behavior of their trajectories when they reach the points of discontinuity.
This description is supplied with the local comparison of the trajectories of
the diffusion processes with those of a skew Brownian motion.
