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2021 Intermittency and infinite variance: the case of integrated supOU processes
Danijel Grahovac, Nikolai N. Leonenko, Murad S. Taqqu
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Electron. J. Probab. 26: 1-31 (2021). DOI: 10.1214/21-EJP623


SupOU processes are superpositions of Ornstein-Uhlenbeck type processes with a random intensity parameter. They are stationary processes whose marginal distribution and dependence structure can be specified independently. Integrated supOU processes have then stationary increments and satisfy central and non-central limit theorems. Their moments, however, can display an unusual behavior known as “intermittency”. We show here that intermittency can also appear when the processes have a heavy tailed marginal distribution and, in particular, an infinite variance.

Funding Statement

Nikolai N. Leonenko was supported in particular by Cardiff Incoming Visiting Fellowship Scheme, International Collaboration Seedcorn Fund, Australian Research Council’s Discovery Projects funding scheme (project DP160101366) and the project MTM2015-71839-P of MINECO, Spain (co-funded with FEDER funds). Murad S. Taqqu was supported in part by the Simons foundation grant 569118 at Boston University. Danijel Grahovac was partially supported by the University of Osijek Grant ZUP2018-31.


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Danijel Grahovac. Nikolai N. Leonenko. Murad S. Taqqu. "Intermittency and infinite variance: the case of integrated supOU processes." Electron. J. Probab. 26 1 - 31, 2021.


Received: 22 October 2019; Accepted: 3 April 2021; Published: 2021
First available in Project Euclid: 3 May 2021

Digital Object Identifier: 10.1214/21-EJP623

Primary: 60F05 , 60G10 , 60G52

Keywords: absolute moments , infinite variance , limit theorems , Ornstein-Uhlenbeck process , supOU processes


Vol.26 • 2021
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