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 (2006) and on the estimates of the Riesz transform given in Bally and Caramellino (Stoch Process Their Appl 121:1332-1355, 2011).
Bally, V., Caramellino, L. (2013). Positivity and Lower Bounds for the Density of Wiener Functionals. POTENTIAL ANALYSIS, 39(2), 141-168 [10.1007/s11118-012-9324-7].
Positivity and Lower Bounds for the Density of Wiener Functionals
CARAMELLINO, LUCIA
2013-01-01
Abstract
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 (2006) and on the estimates of the Riesz transform given in Bally and Caramellino (Stoch Process Their Appl 121:1332-1355, 2011).| File | Dimensione | Formato | |
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