The multifaceted behavior of integrated supOU processes: The infinite variance case

Grahovac, Danijel, Leonenko, Nikolai N. ORCID: https://orcid.org/0000-0003-1932-4091 and Taqqu, Murad S. 2020. The multifaceted behavior of integrated supOU processes: The infinite variance case. Journal of Theoretical Probability 33 , pp. 1801-1831. 10.1007/s10959-019-00935-8

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Abstract

The so-called supOU processes, namely the superpositions of Ornstein–Uhlenbeck type processes, are stationary processes for which one can specify separately the marginal distribution and the temporal dependence structure. They can have finite or infinite variance. We study the limit behavior of integrated infinite variance supOU processes adequately normalized. Depending on the specific circumstances, the limit can be fractional Brownian motion but it can also be a process with infinite variance, a Lévy stable process with independent increments or a stable process with dependent increments. We show that it is even possible to have infinite variance integrated supOU processes converging to processes whose moments are all finite. A number of examples are provided.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Springer Verlag (Germany)
ISSN:	0894-9840
Date of First Compliant Deposit:	25 July 2019
Date of Acceptance:	24 July 2019
Last Modified:	23 Dec 2024 15:45
URI:	https://orca.cardiff.ac.uk/id/eprint/124466

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