On the existence of a time inhomogeneous skew Brownian motion and some related laws

Pierre Etoré (1) , Miguel Martinez (2)

1 MATHFI - Mathématiques financières
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

This article is devoted to the construction of a solution for the "skew inhomogeneous Brownian motion" equation, which first appear in a seminal paper by Sophie Weinryb (1983). We investigate some laws related to the constructed process. In particular, using the description of the straddling excursion above a deterministic time, we compute the joint law of the process, its local time and its straddling time.

Mots clés: Skew Brownian motion; Local time; Straddling excursion

Domaines: Probabilités [math.PR]

Pierre Etoré, Miguel Martinez. On the existence of a time inhomogeneous skew Brownian motion and some related laws. Electronic Journal of Probability, 2012, 17, pp.19:1-27. ⟨10.1214/EJP.v17-1858⟩. ⟨hal-00608221v2⟩