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Malliavin smoothness on the Lévy space with Hölder continuous or BV functionals

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  • Laukkarinen, Eija

Abstract

We consider Malliavin smoothness of random variables f(X1), where X is a pure jump Lévy process and the function f is either bounded and Hölder continuous or of bounded variation. We show that Malliavin differentiability and fractional differentiability of f(X1) depend both on the regularity of f and the Blumenthal–Getoor index of the Lévy measure.

Suggested Citation

  • Laukkarinen, Eija, 2020. "Malliavin smoothness on the Lévy space with Hölder continuous or BV functionals," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4766-4792.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:8:p:4766-4792
    DOI: 10.1016/j.spa.2020.01.016
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    References listed on IDEAS

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    1. Solé, Josep Lluís & Utzet, Frederic & Vives, Josep, 2007. "Canonical Lévy process and Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 117(2), pages 165-187, February.
    2. Rainer Avikainen, 2009. "On irregular functionals of SDEs and the Euler scheme," Finance and Stochastics, Springer, vol. 13(3), pages 381-401, September.
    3. Geiss, Christel & Geiss, Stefan & Gobet, Emmanuel, 2012. "Generalized fractional smoothness and Lp-variation of BSDEs with non-Lipschitz terminal condition," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2078-2116.
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