## Bernoulli

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

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

#### Abstract

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)).

#### Article information

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

Dates
Revised: January 2018
First available in Project Euclid: 12 June 2019

https://projecteuclid.org/euclid.bj/1560326436

Digital Object Identifier
doi:10.3150/18-BEJ1044

Mathematical Reviews number (MathSciNet)
MR3961239

Zentralblatt MATH identifier
07066248

#### Citation

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. https://projecteuclid.org/euclid.bj/1560326436

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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.