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Riesz transform and integration by parts formulas for random variables. (English) Zbl 1229.60069
Integration by parts formulae on the Wiener space enable to prove representation formulae for the distribution laws of variables. In particular, one can write a formula for the density of a variable \(F\), involving the expectation of \(\partial_i Q_d(F-x)\), where \(Q_d\) is the Poisson kernel on \(\mathbb R^d\setminus\{0\}\). A central point of interest in this work is the estimation of \(\mathbb E(|\partial_i Q_d(F-x)|^d)\). As a consequence, regularity and estimates for the density of \(F\) are obtained, and the set where the density is strictly positive is studied.

MSC:
60H07 Stochastic calculus of variations and the Malliavin calculus
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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