## The Annals of Applied Probability

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

#### Abstract

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

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

Dates
First available in Project Euclid: 6 March 2006

https://projecteuclid.org/euclid.aoap/1141654283

Digital Object Identifier
doi:10.1214/105051605000000656

Mathematical Reviews number (MathSciNet)
MR2209338

Zentralblatt MATH identifier
1094.60056

Subjects
Secondary: 65C

#### Citation

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. https://projecteuclid.org/euclid.aoap/1141654283

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