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On infinitely divisible distributions with polynomially decaying characteristic functions

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  • Trabs, Mathias

Abstract

We provide necessary and sufficient conditions on the characteristics of an infinitely divisible distribution under which its characteristic function φ decays polynomially. Under a mild regularity condition this polynomial decay is equivalent to 1/φ being a Fourier multiplier on Besov spaces.

Suggested Citation

  • Trabs, Mathias, 2014. "On infinitely divisible distributions with polynomially decaying characteristic functions," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 56-62.
    • Handle: RePEc:eee:stapro:v:94:y:2014:i:c:p:56-62
    DOI: 10.1016/j.spl.2014.07.002
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    References listed on IDEAS

    as
    1. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 10(4), pages 449-474, December.
    2. Nickl, Richard & Reiß, Markus, 2012. "A Donsker theorem for Lévy measures," SFB 649 Discussion Papers 2012-003, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    3. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 10(4), pages 449-474, December.
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    Cited by:

    1. Jochen Glück & Stefan Roth & Evgeny Spodarev, 2022. "A solution to a linear integral equation with an application to statistics of infinitely divisible moving averages," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1244-1273, September.
    2. Wolfgang Karcher & Stefan Roth & Evgeny Spodarev & Corinna Walk, 2019. "An inverse problem for infinitely divisible moving average random fields," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 263-306, July.
    3. Trabs, Mathias, 2015. "Quantile estimation for Lévy measures," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3484-3521.

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