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In this article we extend the exact simulation methods of Beskos et al. in [4] 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.

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To cite this version:Pierre Etoré, Antoine Lejay. A Donsker theorem to simulate one-dimensional processes with measurable coefficients. ESAIM: Probability and Statistics, EDP Sciences, 2007, 11, pp.301-326 In this paper, we prove a Donker theorem for one-dimensional processes generated by an operator with measurable coefficients. We construct a random walk on any grid on the state space, using the transition probabilities of the approximated process, and the conditional average times it spends on each cell of the grid. Indeed we can compute these quantities by solving some suitable elliptic PDE problems.