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Stable CLTs and Rates for Power Variation of α-Stable Lévy Processes

Author

Listed:
  • Jan M. Gairing

    (Humboldt-Universität zu Berlin)

  • Peter Imkeller

    (Humboldt-Universität zu Berlin)

Abstract

In a central limit type result it has been shown that the pth power variations of an α-stable Lévy process along sequences of equidistant partitions of a given time interval have $\frac{\alpha}{p}$ -stable limits. In this paper we give precise orders of convergence for the distances of the approximate power variations computed for partitions with mesh of order $\frac{1}{n}$ and the limiting law, measured in terms of the Kolmogorov-Smirnov metric. In case 2α

Suggested Citation

  • Jan M. Gairing & Peter Imkeller, 2015. "Stable CLTs and Rates for Power Variation of α-Stable Lévy Processes," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 73-90, March.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:1:d:10.1007_s11009-013-9378-z
    DOI: 10.1007/s11009-013-9378-z
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