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Local asymptotic self-similarity for heavy-tailed harmonizable fractional Lévy motions

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Local asymptotic self-similarity for heavy-tailed harmonizable fractional Lévy motions. / Basse-O'Connor, Andreas; Grønbæk, Thorbjørn Øystein Brynimin; Podolskij, Mark.

In: ESAIM: Probability & Statistics, Vol. 25, 07.2021, p. 286-297.

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Author

Basse-O'Connor, Andreas ; Grønbæk, Thorbjørn Øystein Brynimin ; Podolskij, Mark. / Local asymptotic self-similarity for heavy-tailed harmonizable fractional Lévy motions. In: ESAIM: Probability & Statistics. 2021 ; Vol. 25. pp. 286-297.

Bibtex

@article{18e4687c68744bc4bd5794932ba1c0b1,
title = "Local asymptotic self-similarity for heavy-tailed harmonizable fractional L{\'e}vy motions",
abstract = "In this work we characterize the local asymptotic self-similarity of harmonizable fractional L{\'e}vy 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 L{\'e}vy motions.",
keywords = "Fractional processes, Harmonizable processes, Local asymptotic self-similarity, Spectral representations",
author = "Andreas Basse-O'Connor and Gr{\o}nb{\ae}k, {Thorbj{\o}rn {\O}ystein Brynimin} and Mark Podolskij",
year = "2021",
month = jul,
doi = "10.1051/ps/2021011",
language = "English",
volume = "25",
pages = "286--297",
journal = "ESAIM: Probability & Statistics",
issn = "1292-8100",
publisher = "E D P Sciences",

}

RIS

TY - JOUR

T1 - Local asymptotic self-similarity for heavy-tailed harmonizable fractional Lévy motions

AU - Basse-O'Connor, Andreas

AU - Grønbæk, Thorbjørn Øystein Brynimin

AU - Podolskij, Mark

PY - 2021/7

Y1 - 2021/7

N2 - 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.

AB - 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.

KW - Fractional processes

KW - Harmonizable processes

KW - Local asymptotic self-similarity

KW - Spectral representations

U2 - 10.1051/ps/2021011

DO - 10.1051/ps/2021011

M3 - Journal article

VL - 25

SP - 286

EP - 297

JO - ESAIM: Probability & Statistics

JF - ESAIM: Probability & Statistics

SN - 1292-8100

ER -