A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients

Details A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients

2006-03-09

arxiv.org/abs/math/0603214v1

Annals of Applied Probability 2006, Vol. 16, No. 1, 107-139

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051605000000656 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051605000000656

The aim of this article is to provide a scheme for simulating diffusion processes evolving in one-dimensional discontinuous media. This scheme does not rely on smoothing the coefficients that appear in the infinitesimal generator of the diffusion processes, but uses instead an exact description of the behavior of their trajectories when they reach the points of discontinuity. This description is supplied with the local comparison of the trajectories of the diffusion processes with those of a skew Brownian motion.

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