We use integration by parts formulas to give estimates for the L p norm of the Riesz transform. This is motivated by the representation formula for conditional expectations of functionals on the Wiener space already given in Malliavin and Thalmaier (2006). As a consequence, we obtain regularity and estimates for the density of non-degenerated functionals on the Wiener space. We also give a semi-distance which characterizes the convergence to the boundary of the set of the strict positivity points for the density.

Bally, V., Caramellino, L. (2011). Riesz transform and integration by parts formulas for random variables. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 121(6), 1332-1366 [10.1016/j.spa.2011.02.006,].

Riesz transform and integration by parts formulas for random variables

CARAMELLINO, LUCIA
2011-01-01

Abstract

We use integration by parts formulas to give estimates for the L p norm of the Riesz transform. This is motivated by the representation formula for conditional expectations of functionals on the Wiener space already given in Malliavin and Thalmaier (2006). As a consequence, we obtain regularity and estimates for the density of non-degenerated functionals on the Wiener space. We also give a semi-distance which characterizes the convergence to the boundary of the set of the strict positivity points for the density.
2011
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA
English
Riesz transform; Integration by parts; Malliavin calculus; Sobolev spaces
Bally, V., Caramellino, L. (2011). Riesz transform and integration by parts formulas for random variables. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 121(6), 1332-1366 [10.1016/j.spa.2011.02.006,].
Bally, V; Caramellino, L
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/40300
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