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 Probability Surveys > Vol. 3 (2006) open journal systems 


On the constructions of the skew Brownian motion

Antoine Lejay, Projet OMEGA, INRIA


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.

AMS 2000 subject classifications: Primary 60J60; secondary 60H10, 60J55.

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.

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Lejay, Antoine, On the constructions of the skew Brownian motion, Probability Surveys, 3, (2006), 413-466 (electronic).

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