Probability Surveys

On the constructions of the skew Brownian motion

Antoine Lejay

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Abstract

This article summarizes the various ways one may use to construct the Skew Brownian motion, and shows their connections. Recent applications of this process in modelling and numerical simulation motivates this survey. This article ends with a brief account of related results, extensions and applications of the Skew Brownian motion.

Article information

Source
Probab. Surveys Volume 3 (2006), 413-466.

Dates
First available in Project Euclid: 8 January 2007

Permanent link to this document
http://projecteuclid.org/euclid.ps/1168268869

Digital Object Identifier
doi:10.1214/154957807000000013

Mathematical Reviews number (MathSciNet)
MR2280299

Zentralblatt MATH identifier
1189.60145

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60J55: Local time and additive functionals

Keywords
skew Brownian motion PDE with singular drift PDE with transmission condition SDE with local time excursions of Brownian motion scale function and speed measure mathematical modelling Monte Carlo methods

Citation

Lejay, Antoine. On the constructions of the skew Brownian motion. Probab. Surveys 3 (2006), 413--466. doi:10.1214/154957807000000013. http://projecteuclid.org/euclid.ps/1168268869.


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