The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 16, Number 1 (2006), 107-139.
A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients
Antoine Lejay and Miguel Martinez
Full-text: Open access
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
https://projecteuclid.org/euclid.aoap/1141654283
Digital Object Identifier
doi:10.1214/105051605000000656
Mathematical Reviews number (MathSciNet)
MR2209338
Zentralblatt MATH identifier
1094.60056
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. https://projecteuclid.org/euclid.aoap/1141654283.
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