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On generalized Malliavin calculus


  • Lototsky, S.V.
  • Rozovskii, B.L.
  • Seleši, D.


The Malliavin derivative, the divergence operator (Skorokhod integral), and the Ornstein–Uhlenbeck operator are extended from the traditional Gaussian setting to nonlinear generalized functionals of white noise. These extensions are related to the new developments in the theory of stochastic PDEs, in particular elliptic PDEs driven by spatial white noise and quantized nonlinear equations.

Suggested Citation

  • Lototsky, S.V. & Rozovskii, B.L. & Seleši, D., 2012. "On generalized Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 808-843.
  • Handle: RePEc:eee:spapps:v:122:y:2012:i:3:p:808-843 DOI: 10.1016/

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    References listed on IDEAS

    1. Pipiras, Vladas, 2007. "Nonminimal sets, their projections and integral representations of stable processes," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1285-1302, September.
    2. Cambanis, Stamatis & Maejima, Makoto & Samorodnitsky, Gennady, 1992. "Characterization of linear and harmonizable fractional stable motions," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 91-110, August.
    3. Cambanis, Stamatis & Hardin, Clyde D. & Weron, Aleksander, 1987. "Ergodic properties of stationary stable processes," Stochastic Processes and their Applications, Elsevier, vol. 24(1), pages 1-18, February.
    4. Hardin, Clyde D., 1982. "On the spectral representation of symmetric stable processes," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 385-401, September.
    5. Wang, Yizao & Stoev, Stilian A., 2010. "On the association of sum- and max-stable processes," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 480-488, March.
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