A Poincaré cone condition in the Poincaré group

Camille Tardif (1)

1 IRMA - Institut de Recherche Mathématique Avancée

Gradinaru and Ben Arous described the behavior of the Green function of a sub-elliptic diffusion. We adapt their proof in the general setting of an hypoelliptic diffusion and deduce a Wiener criterion and a Poincaré cone condition of thinness for a relativistic diffusion in the Poincaré group introduced by Dudley.

Mots clés: fine topology; Green function; hypoelliptic operator; relativistic diffusion; Wiener criterion

Domaines: Probabilités [math.PR]

Camille Tardif. A Poincaré cone condition in the Poincaré group. Potential Analysis, 2013, ⟨10.1007/s11118-012-9304-y⟩. ⟨hal-00661960v2⟩