• Bernoulli
  • Volume 25, Number 3 (2019), 2029-2050.

The unusual properties of aggregated superpositions of Ornstein–Uhlenbeck type processes

Danijel Grahovac, Nikolai N. Leonenko, Alla Sikorskii, and Murad S. Taqqu

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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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Bernoulli, Volume 25, Number 3 (2019), 2029-2050.

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

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cumulants intermittency moments Ornstein–Uhlenbeck process self-similarity supOU processes


Grahovac, Danijel; Leonenko, Nikolai N.; Sikorskii, Alla; Taqqu, Murad S. The unusual properties of aggregated superpositions of Ornstein–Uhlenbeck type processes. Bernoulli 25 (2019), no. 3, 2029--2050. doi:10.3150/18-BEJ1044.

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Supplemental materials

  • Supplement to “The unusual properties of aggregated superpositions of Ornstein– Uhlenbeck type processes”. The supplement contains the proofs of the results not proved in the paper.