Abstract
In this note, we provide a simulation algorithm for a diffusion process in a layered media. Our main tools are the properties of the Skew Brownian motion and a path decomposition technique for simulating occupation times.
Highlights
Simulation of diffusion processes in multi-dimensional discontinuous media is still a challenging problem, while recent progresses have been done for one-dimensional media
The object of this note is to deal with the simulation of the stochastic process generated by the divergence form operator
This could be used for example to model a solute in a vertically layered porous media submitted to a advective flow U and diffusion effects given by D [1, 34, 35, 37]
Summary
Simulation of diffusion processes in multi-dimensional discontinuous media is still a challenging problem, while recent progresses have been done for one-dimensional media. The simulation of one-dimensional stochastic processes generated by a divergence form operator with discontinuous coefficients has been the subject of a large literature and several algorithms have been proposed (See [23, 7, 8, 9, 13, 15, 22, 27, 28, 37, 40] for a non-exhaustive list of possible algorithms). Some of these schemes generate random variates with the true distribution of X t. Θ given in Eq (3) shall be changed into −θ in Eq (4) (See [22])
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