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Multidimensional Lévy white noise in weighted Besov spaces

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  • Fageot, Julien
  • Fallah, Alireza
  • Unser, Michael

Abstract

In this paper, we study the Besov regularity of a general d-dimensional Lévy white noise. More precisely, we describe new sample paths properties of a given noise in terms of weighted Besov spaces. In particular, we characterize the smoothness and integrability properties of the noise using the indices introduced by Blumenthal, Getoor, and Pruitt. Our techniques rely on wavelet methods and generalized moments estimates for Lévy noises.

Suggested Citation

  • Fageot, Julien & Fallah, Alireza & Unser, Michael, 2017. "Multidimensional Lévy white noise in weighted Besov spaces," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1599-1621.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:5:p:1599-1621
    DOI: 10.1016/j.spa.2016.08.011
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    References listed on IDEAS

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    1. Rosenbaum, Mathieu, 2009. "First order p-variations and Besov spaces," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 55-62, January.
    2. Deng, Chang-Song & Schilling, René L., 2015. "On shift Harnack inequalities for subordinate semigroups and moment estimates for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3851-3878.
    3. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68.
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    Cited by:

    1. Julien Fageot & Michael Unser, 2019. "Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Lévy White Noises," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1166-1189, September.
    2. Julien Fageot & Michael Unser & John Paul Ward, 2020. "The $$n$$n-term Approximation of Periodic Generalized Lévy Processes," Journal of Theoretical Probability, Springer, vol. 33(1), pages 180-200, March.
    3. Fageot, Julien & Humeau, Thomas, 2021. "The domain of definition of the Lévy white noise," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 75-102.

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