Lejay, Antoine On the constructions of the skew Brownian motion. (English) Zbl 1189.60145 Probab. Surv. 3, 413-466 (2006). Summary: 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 modeling and numerical simulation motivates this survey. This article ends with a brief account of related results, extensions and applications of the skew Brownian motion. Cited in 104 Documents MSC: 60J60 Diffusion processes 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60J55 Local time and additive functionals 60J65 Brownian motion 60-02 Research exposition (monographs, survey articles) pertaining to probability theory 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 modeling; Monte Carlo methods PDFBibTeX XMLCite \textit{A. Lejay}, Probab. Surv. 3, 413--466 (2006; Zbl 1189.60145) Full Text: DOI arXiv EuDML