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Multifractality of products of geometric Ornstein-Uhlenbeck-type processes

Anh, V. V., Leonenko, Nikolai N. ORCID: and Shieh, N. 2008. Multifractality of products of geometric Ornstein-Uhlenbeck-type processes. Advances in Applied Probability 40 (4) , pp. 1129-1156. 10.1239/aap/1231340167

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We investigate the properties of multifractal products of geometric Ornstein-Uhlenbeck (OU) processes driven by Lévy motion. The conditions on the mean, variance, and covariance functions of the resulting cumulative processes are interpreted in terms of the moment generating functions. We consider five cases of infinitely divisible distributions for the background driving Lévy processes, namely, the gamma and variance gamma distributions, the inverse Gaussian and normal inverse Gaussian distributions, and the z-distributions. We establish the corresponding scenarios for the limiting processes, including their Rényi functions and dependence structure.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: Multifractal products; long-range dependence; geometric Ornstein-Uhlenbeck process; Lévy process; infinitely divisible distribution
Publisher: Applied Probability Trust
ISSN: 0001-8678
Last Modified: 19 Oct 2022 08:41

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