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

Author

Listed:
  • Danijel Grahovac

    (University of Osijek)

  • Nikolai N. Leonenko

    (Cardiff University)

  • Murad S. Taqqu

    (Boston University)

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.

Suggested Citation

  • Danijel Grahovac & Nikolai N. Leonenko & Murad S. Taqqu, 2020. "The Multifaceted Behavior of Integrated supOU Processes: The Infinite Variance Case," Journal of Theoretical Probability, Springer, vol. 33(4), pages 1801-1831, December.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:4:d:10.1007_s10959-019-00935-8
    DOI: 10.1007/s10959-019-00935-8
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    References listed on IDEAS

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    1. Grahovac, Danijel & Leonenko, Nikolai N. & Taqqu, Murad S., 2019. "Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5113-5150.
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    Cited by:

    1. Grahovac, Danijel, 2022. "Intermittency in the small-time behavior of Lévy processes," Statistics & Probability Letters, Elsevier, vol. 187(C).

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