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Small-time moment asymptotics for Lévy processes

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  • Figueroa-López, José E.

Abstract

Conditions ensuring that are given for a Lévy process X with Lévy measure [nu] and for unbounded moment functions f. Compared with previous works, the moment functions considered here satisfy very mild conditions aimed at controlling how fast f grows at infinity. As an application of our results, the infinitesimal generator of the Lévy process is shown to be well-defined in a class of smooth unbounded functions equipped with a suitable norm. Also, the rate of convergence is studied when f is a smooth function vanishing in a neighborhood of the origin.

Suggested Citation

  • Figueroa-López, José E., 2008. "Small-time moment asymptotics for Lévy processes," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3355-3365, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:18:p:3355-3365
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Woerner Jeannette H. C., 2003. "Variational sums and power variation: a unifying approach to model selection and estimation in semimartingale models," Statistics & Risk Modeling, De Gruyter, vol. 21(1), pages 47-68, January.
    3. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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    Cited by:

    1. Kappus, Johanna, 2012. "Nonparametric adaptive estimation of linear functionals for low frequency observed Lévy processes," SFB 649 Discussion Papers 2012-016, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    2. repec:hum:wpaper:sfb649dp2012-016 is not listed on IDEAS
    3. Kappus, Johanna & Reiß, Markus, 2010. "Estimation of the characteristics of a Lévy process observed at arbitrary frequency," SFB 649 Discussion Papers 2010-015, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    4. Hoffmann, Michael & Vetter, Mathias, 2017. "Weak convergence of the empirical truncated distribution function of the Lévy measure of an Itō semimartingale," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1517-1543.

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