Positivity and lower bounds for the density of Wiener functionals

Vlad Bally (1, 2) , Lucia Caramellino (3)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 MATHRISK - Mathematical Risk handling
3 Dipartimento di Matematica [Rome]

We consider a functional on the Wiener space which is smooth and not degenerated in Malliavin sense and we give a criterion for the strict positivity of the density, that we can use to state lower bounds as well. The results are based on the representation of the density in terms of the Riesz transform introduced in Malliavin and Thalmaier [17] and on the estimates of the Riesz transform given in Bally and Caramellino [3]

Mots clés: Riesz transform; Malliavin calculus; Strict positivity and lower bounds for the density; 60H07; 60H30

Domaines: Probabilités [math.PR]

Vlad Bally, Lucia Caramellino. Positivity and lower bounds for the density of Wiener functionals. Potential Analysis, 2013, 39 (2), pp.141-168. ⟨10.1007/s11118-012-9324-7⟩. ⟨hal-00936148⟩