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

Jan M. Gairing () and Peter Imkeller ()
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Jan M. Gairing: Humboldt-Universität zu Berlin
Peter Imkeller: Humboldt-Universität zu Berlin

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 1, 73-90

Abstract: 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

Keywords: Lévy process; Stable process; Power variation; Central limit theorem; Fourier transform; Tail probability; Rate of convergence; Empirical distribution function; Minimum distance estimator; Brownian bridge; Primary 60G51; Secondary 60G52; 60H30; 42A38; 62G30 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s11009-013-9378-z

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