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Riesz transform and integration by parts formulas for random variables

Author

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  • Bally, Vlad
  • Caramellino, Lucia

Abstract

We use integration by parts formulas to give estimates for the Lp 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)Â [13]. 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.

Suggested Citation

  • Bally, Vlad & Caramellino, Lucia, 2011. "Riesz transform and integration by parts formulas for random variables," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1332-1355, June.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:6:p:1332-1355
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    Cited by:

    1. Löcherbach, E., 2018. "Absolute continuity of the invariant measure in piecewise deterministic Markov Processes having degenerate jumps," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 1797-1829.
    2. Likibi Pellat, Rhoss & Menoukeu Pamen, Olivier, 2024. "Density analysis for coupled forward–backward SDEs with non-Lipschitz drifts and applications," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    3. He, Kai & Ren, Jiagang & Zhang, Hua, 2014. "Localization of Wiener functionals of fractional regularity and applications," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2543-2582.

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