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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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

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1141654283

Digital Object Identifier
doi:10.1214/105051605000000656

Mathematical Reviews number (MathSciNet)
MR2209338

Zentralblatt MATH identifier
05036877

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

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

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


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