  In this article we extend the exact simulation methods of Beskos et al. to
the solutions of one-dimensional stochastic differential equations involving
the local time of the unknown process at point zero. In order to perform the
method we compute the law of the skew Brownian motion with drift. The method
presented in this article covers the case where the solution of the SDE with
local time corresponds to a divergence form operator with a discontinuous
coefficient at zero. Numerical examples are shown to illustrate the method and
the performances are compared with more traditional discretization schemes.

Probability