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Quasi Ornstein-Uhlenbeck processes

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Quasi Ornstein-Uhlenbeck processes. / Barndorff-Nielsen, Ole Eiler; Basse-O'Connor, Andreas.

I: Bernoulli, Bind 17, Nr. 3, 2011, s. 916-941.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

Harvard

Barndorff-Nielsen, OE & Basse-O'Connor, A 2011, 'Quasi Ornstein-Uhlenbeck processes', Bernoulli, bind 17, nr. 3, s. 916-941. https://doi.org/10.3150/10-BEJ311

APA

Barndorff-Nielsen, O. E., & Basse-O'Connor, A. (2011). Quasi Ornstein-Uhlenbeck processes. Bernoulli, 17(3), 916-941. https://doi.org/10.3150/10-BEJ311

CBE

MLA

Barndorff-Nielsen, Ole Eiler og Andreas Basse-O'Connor. "Quasi Ornstein-Uhlenbeck processes". Bernoulli. 2011, 17(3). 916-941. https://doi.org/10.3150/10-BEJ311

Vancouver

Barndorff-Nielsen OE, Basse-O'Connor A. Quasi Ornstein-Uhlenbeck processes. Bernoulli. 2011;17(3):916-941. doi: 10.3150/10-BEJ311

Author

Barndorff-Nielsen, Ole Eiler ; Basse-O'Connor, Andreas. / Quasi Ornstein-Uhlenbeck processes. I: Bernoulli. 2011 ; Bind 17, Nr. 3. s. 916-941.

Bibtex

@article{8fac9b701ba211dfb95d000ea68e967b,
title = "Quasi Ornstein-Uhlenbeck processes",
abstract = "The question of existence and properties of stationary solutions to Langevin equations driven by noise processes with stationary increments is discussed, with particular focus on noise processes of pseudo-moving-average type. On account of the Wold–Karhunen decomposition theorem, such solutions are, in principle, representable as a moving average (plus a drift-like term) but the kernel in the moving average is generally not available in explicit form. A class of cases is determined where an explicit expression of the kernel can be given, and this is used to obtain information on the asymptotic behavior of the associated autocorrelation functions, both for small and large lags. Applications to Gaussian- and L{\'e}vy-driven fractional Ornstein–Uhlenbeck processes are presented. A Fubini theorem for L{\'e}vy bases is established as an element in the derivations.",
author = "Barndorff-Nielsen, {Ole Eiler} and Andreas Basse-O'Connor",
year = "2011",
doi = "10.3150/10-BEJ311",
language = "English",
volume = "17",
pages = "916--941",
journal = "Bernoulli",
issn = "1350-7265",
publisher = "International Statistical Institute",
number = "3",

}

RIS

TY - JOUR

T1 - Quasi Ornstein-Uhlenbeck processes

AU - Barndorff-Nielsen, Ole Eiler

AU - Basse-O'Connor, Andreas

PY - 2011

Y1 - 2011

N2 - The question of existence and properties of stationary solutions to Langevin equations driven by noise processes with stationary increments is discussed, with particular focus on noise processes of pseudo-moving-average type. On account of the Wold–Karhunen decomposition theorem, such solutions are, in principle, representable as a moving average (plus a drift-like term) but the kernel in the moving average is generally not available in explicit form. A class of cases is determined where an explicit expression of the kernel can be given, and this is used to obtain information on the asymptotic behavior of the associated autocorrelation functions, both for small and large lags. Applications to Gaussian- and Lévy-driven fractional Ornstein–Uhlenbeck processes are presented. A Fubini theorem for Lévy bases is established as an element in the derivations.

AB - The question of existence and properties of stationary solutions to Langevin equations driven by noise processes with stationary increments is discussed, with particular focus on noise processes of pseudo-moving-average type. On account of the Wold–Karhunen decomposition theorem, such solutions are, in principle, representable as a moving average (plus a drift-like term) but the kernel in the moving average is generally not available in explicit form. A class of cases is determined where an explicit expression of the kernel can be given, and this is used to obtain information on the asymptotic behavior of the associated autocorrelation functions, both for small and large lags. Applications to Gaussian- and Lévy-driven fractional Ornstein–Uhlenbeck processes are presented. A Fubini theorem for Lévy bases is established as an element in the derivations.

U2 - 10.3150/10-BEJ311

DO - 10.3150/10-BEJ311

M3 - Journal article

VL - 17

SP - 916

EP - 941

JO - Bernoulli

JF - Bernoulli

SN - 1350-7265

IS - 3

ER -