Fractional processes; Harmonizable processes; Local asymptotic self-similarity; Spectral representations; Fractional stable motion; Heavy-tailed; Local asymptotic; Self-similarities; Tangent process; Statistics and Probability
Abstract :
[en] In this work we characterize the local asymptotic self-similarity of harmonizable fractional Lévy motions in the heavy tailed case. The corresponding tangent process is shown to be the harmonizable fractional stable motion. In addition, we provide sufficient conditions for existence of harmonizable fractional Lévy motions.
Disciplines :
Mathematics
Author, co-author :
Basse-O'connor, Andreas; Department of Mathematics, Aarhus University, Aarhus, Denmark
Grønbæk, Thorbjørn; Department of Mathematics, Aarhus University, Aarhus, Denmark
PODOLSKIJ, Mark ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) ; Department of Mathematics, Aarhus University, Aarhus, Denmark
External co-authors :
yes
Language :
English
Title :
Local asymptotic self-similarity for heavy tailed harmonizable fractional Lévy motions
H2020 - 815703 - STAMFORD - Statistical Methods For High Dimensional Diffusions
Funders :
ERC - European Research Council Union Européenne
Funding number :
815703
Funding text :
Acknowledgements. A. Basse-O’Connor and T. Grønbæk’s research were supported by the grant DFF-4002-00003 from the Danish Council for Independent Research. M. Podolskij gratefully acknowledges financial support through the research project “Ambit fields: probabilistic properties and statistical inference” funded by Villum Fonden. Finally, we would like to thank an anonymous referee for very detailed and constructive remarks and corrections.
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