Hölder norms and the support theorem for diffusions

Gérard Ben Arous (1) , Mihai Gradinaru (2) , Michel Ledoux (3)

1 IMA - Institut de Mathématiques
2 IECN - Institut Élie Cartan de Nancy
3 LSP - Laboratoire de Statistique et Probabilités

One shows that the Stroock-Varadhan support theorem is valid in $\alpha$-Hölder norm. The central tool is an estimate of the probability that the Brownian motion has a large Hölder norm but a small uniform norm.

Mots clés: diffusion processes; support theorem; Brownian motion; Hölder norm; gaussian measures

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Gérard Ben Arous, Mihai Gradinaru, Michel Ledoux. Hölder norms and the support theorem for diffusions. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 1994, 30, pp.415-436. ⟨hal-00120184⟩