Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes

Grahovac, Danijel, Leonenko, Nikolai N. ORCID: https://orcid.org/0000-0003-1932-4091 and Taqqu, Murad S. 2019. Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes. Stochastic Processes and their Applications 129 (12) , pp. 5113-5150. 10.1016/j.spa.2019.01.010

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Abstract

Superpositions of Ornstein–Uhlenbeck type (supOU) processes provide a rich class of stationary stochastic processes for which the marginal distribution and the dependence structure may be modeled independently. We show that they can also display intermittency, a phenomenon affecting the rate of growth of moments. To do so, we investigate the limiting behavior of integrated supOU processes with finite variance. After suitable normalization four different limiting processes may arise depending on the decay of the correlation function and on the characteristic triplet of the marginal distribution. To show that supOU processes may exhibit intermittency, we establish the rate of growth of moments for each of the four limiting scenarios. The rate change indicates that there is intermittency, which is expressed here as a change-point in the asymptotic behavior of the absolute moments.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Elsevier
ISSN:	0304-4149
Date of First Compliant Deposit:	1 February 2019
Date of Acceptance:	31 January 2019
Last Modified:	16 Nov 2024 22:15
URI:	https://orca.cardiff.ac.uk/id/eprint/119124

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