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August 2011 Quasi Ornstein–Uhlenbeck processes
Ole E. Barndorff-Nielsen, Andreas Basse-O’Connor
Bernoulli 17(3): 916-941 (August 2011). DOI: 10.3150/10-BEJ311


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.


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Ole E. Barndorff-Nielsen. Andreas Basse-O’Connor. "Quasi Ornstein–Uhlenbeck processes." Bernoulli 17 (3) 916 - 941, August 2011.


Published: August 2011
First available in Project Euclid: 7 July 2011

zbMATH: 1233.60020
MathSciNet: MR2817611
Digital Object Identifier: 10.3150/10-BEJ311

Keywords: fractional Ornstein–Uhlenbeck processes , Fubini theorem for Lévy bases , Langevin equations , Stationary processes

Rights: Copyright © 2011 Bernoulli Society for Mathematical Statistics and Probability

Vol.17 • No. 3 • August 2011
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