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Simulating diffusion processes in discontinuous media: a numerical scheme with constant time steps. (English) Zbl 1284.65007
Summary: In this article, we propose new Monte Carlo techniques for moving a diffusive particle in a discontinuous media. In this framework, we characterize the stochastic process that governs the positions of the particle. The key tool is the reduction of the process to a Skew Brownian motion (SBM). In a zone where the coefficients are locally constant on each side of the discontinuity, the new position of the particle after a constant time step is sampled from the exact distribution of the SBM process at the considered time. To do so, we propose two different but equivalent algorithms: a two-steps simulation with a stop at the discontinuity and a one-step direct simulation of the SBM dynamic. Some benchmark tests illustrate their effectiveness.

65C05 Monte Carlo methods
76R50 Diffusion
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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