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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.

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