The Annals of Applied Probability

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

Antoine Lejay and Miguel Martinez

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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.

Article information

Ann. Appl. Probab. Volume 16, Number 1 (2006), 107-139.

First available in Project Euclid: 6 March 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 65C

Monte Carlo methods skew Brownian motion divergence form operator one-dimensional diffusion local time scale function speed measure


Lejay, Antoine; Martinez, Miguel. A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients. Ann. Appl. Probab. 16 (2006), no. 1, 107--139. doi:10.1214/105051605000000656.

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