The Multifaceted Behavior of Integrated supOU Processes: The Infinite Variance Case

Danijel Grahovac (), Nikolai N. Leonenko () and Murad S. Taqqu ()
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Danijel Grahovac: University of Osijek
Nikolai N. Leonenko: Cardiff University
Murad S. Taqqu: Boston University

Journal of Theoretical Probability, 2020, vol. 33, issue 4, 1801-1831

Abstract: 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.

Keywords: supOU processes; Ornstein–Uhlenbeck process; Limit theorems; Infinite variance; Stable processes; 60F05; 60G52; 60G10 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-019-00935-8

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