caa a22 4500 605519420 CHVBK 20210128100730.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s11009-013-9378-z doi (NATIONALLICENCE)springer-10.1007/s11009-013-9378-z Stable CLTs and Rates for Power Variation of α -Stable Lévy Processes [Elektronische Daten] [Jan Gairing, Peter Imkeller] 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 < p the convergence rate is seen to be of order $\frac{1}{n}$ , in case α < p < 2α the order is $n^{1-\frac{p}{\alpha}}.$ Springer Science+Business Media New York, 2013 Lévy process nationallicence Stable process nationallicence Power variation nationallicence Central limit theorem nationallicence Fourier transform nationallicence Tail probability nationallicence Rate of convergence nationallicence Empirical distribution function nationallicence Minimum distance estimator nationallicence Brownian bridge nationallicence Gairing Jan Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany aut Imkeller Peter Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany aut Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/1(2015-03-01), 73-90 1387-5841 17:1<73 2015 17 11009 https://doi.org/10.1007/s11009-013-9378-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11009-013-9378-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gairing Jan Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany aut NATIONALLICENCE 700 1- Imkeller Peter Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany aut NATIONALLICENCE 773 0- Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/1(2015-03-01), 73-90 1387-5841 17:1<73 2015 17 11009