High frequency data; local time; mixed normal distribution; occupation time; stable Lévy processes; Statistics and Probability; Modeling and Simulation; Statistics, Probability and Uncertainty
Résumé :
[en] A novel theoretical result on estimation of the local time and the occupation time measure of an α-stable Lévy process with α ∈ (1, 2) is presented. The approach is based upon computing the conditional expectation of the desired quantities given high frequency data, which is an L2-optimal statistic by construction. The corresponding stable central limit theorems are proved and a statistical application is discussed. In particular, this work extends the results of [20], which investigated the case of the Brownian motion.
Disciplines :
Mathématiques
Auteur, co-auteur :
AMORINO, Chiara ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Mathematics > Team Mark PODOLSKIJ
Jaramillo, Arturo; Research in Mathematics (CIMAT), Valenciana, Mexico
PODOLSKIJ, Mark ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
Optimal estimation of the local time and the occupation time measure for an α-stable Lévy process
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