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Stochastic Analysis: A Series of LecturesIntegration by Parts Formulas and Regularity of Probability Laws

Stochastic Analysis: A Series of Lectures: Integration by Parts Formulas and Regularity of... [We present an abstract setting for integration by parts inspired by the Malliavin calculus. In this framework we give the so-called Malliavin–Thalmaier formula which allows us to represent the density of the law of a multi-dimensional random variable using just one integration by parts, and we investigate the properties of the density using this formula. Finally we present a new argument, based on an interpolation method, which permits us to obtain regularity properties for the density under quite weak regularity assumptions.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Stochastic Analysis: A Series of LecturesIntegration by Parts Formulas and Regularity of Probability Laws

Part of the Progress in Probability Book Series (volume 68)
Editors: Dalang, Robert C.; Dozzi, Marco; Flandoli, Franco; Russo, Francesco
Bally, Vlad
Stochastic Analysis: A Series of Lectures — May 15, 2015
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References (1)

Publisher
Springer Basel
Copyright
© Springer Basel 2015
ISBN
978-3-0348-0908-5
Pages
77 –100
DOI
10.1007/978-3-0348-0909-2_3
Publisher site
See Chapter on Publisher Site

Abstract

[We present an abstract setting for integration by parts inspired by the Malliavin calculus. In this framework we give the so-called Malliavin–Thalmaier formula which allows us to represent the density of the law of a multi-dimensional random variable using just one integration by parts, and we investigate the properties of the density using this formula. Finally we present a new argument, based on an interpolation method, which permits us to obtain regularity properties for the density under quite weak regularity assumptions.]

Published: May 15, 2015

Keywords: Integration by parts; Malliavin calculus; Riesz transform; Interpolation; 60H07; 60F05

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