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.
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© 2015 Springer Basel
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Bally, V. (2015). Integration by Parts Formulas and Regularity of Probability Laws. In: Dalang, R., Dozzi, M., Flandoli, F., Russo, F. (eds) Stochastic Analysis: A Series of Lectures. Progress in Probability, vol 68. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0909-2_3
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DOI: https://doi.org/10.1007/978-3-0348-0909-2_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0908-5
Online ISBN: 978-3-0348-0909-2
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