Pénalisations of Walsh's Brownian motion

Joseph Najnudel (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

In this paper, we construct a family of probability measures, by penalizations of a Walsh's Brownian motion with a weight dependent on its value and its local time at a time t. We prove that this family converges to a probability measure as t tends to infinity, and we study the behaviour of this limit measure.

Mots clés: penalization; local time; Walsh's Brownian motion

Domaines: Probabilités [math.PR]

Joseph Najnudel. Pénalisations of Walsh's Brownian motion. 2005. ⟨hal-00005413⟩