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August 2019 The unusual properties of aggregated superpositions of Ornstein–Uhlenbeck type processes
Danijel Grahovac, Nikolai N. Leonenko, Alla Sikorskii, Murad S. Taqqu
Bernoulli 25(3): 2029-2050 (August 2019). DOI: 10.3150/18-BEJ1044


Superpositions of Ornstein–Uhlenbeck type (supOU) processes form a rich class of stationary processes with a flexible dependence structure. The asymptotic behavior of the integrated and partial sum supOU processes can be, however, unusual. Their cumulants and moments turn out to have an unexpected rate of growth. We identify the property of fast growth of moments or cumulants as intermittency. Many proofs are given in a supplemental article (Grahovac, Leonenko, Sikorskii and Taqqu (2018)).


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Danijel Grahovac. Nikolai N. Leonenko. Alla Sikorskii. Murad S. Taqqu. "The unusual properties of aggregated superpositions of Ornstein–Uhlenbeck type processes." Bernoulli 25 (3) 2029 - 2050, August 2019.


Received: 1 August 2017; Revised: 1 January 2018; Published: August 2019
First available in Project Euclid: 12 June 2019

zbMATH: 07066248
MathSciNet: MR3961239
Digital Object Identifier: 10.3150/18-BEJ1044

Keywords: Cumulants , Intermittency , moments , Ornstein–Uhlenbeck process , self-similarity , supOU processes

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability


Vol.25 • No. 3 • August 2019
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