On the Constructions of the Skew Brownian Motion

Antoine Lejay (1, 2)

1 OMEGA - Probabilistic numerical methods
2 IECN - Institut Élie Cartan de Nancy

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.

Mots clés: 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

Domaines: Probabilités [math.PR]

Antoine Lejay. On the Constructions of the Skew Brownian Motion. Probability Surveys, 2006, 3, pp.413-466. ⟨10.1214/154957807000000013⟩. ⟨inria-00000785v2⟩