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Asymptotics of the Cross-Variation of Young Integrals with Respect to a General Self-Similar Gaussian Process

Authors
  • Douissi, Soukaina1, 2
  • Es-Sebaiy, Khalifa3
  • Moussaten, Soufiane4
  • 1 University Cadi Ayyad, Marrakech, 40000, Morocco , Marrakech (Morocco)
  • 2 Michigan State University, East Lansing, MI, 48824, USA , East Lansing (United States)
  • 3 Kuwait University, Kuwait, Kuwait , Kuwait (Kuwait)
  • 4 Faculty of Sciences Mohamed first University, Oujda, Morocco , Oujda (Morocco)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Oct 10, 2020
Volume
40
Issue
6
Pages
1941–1960
Identifiers
DOI: 10.1007/s10473-020-0621-8
Source
Springer Nature
Keywords
License
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Abstract

We show in this work that the limit in law of the cross-variation of processes having the form of Young integral with respect to a general self-similar centered Gaussian process of order β ∈ (1/2, 3/4] is normal according to the values of β. We apply our results to two self-similar Gaussian processes: the subfractional Brownian motion and the bifractional Brownian motion.

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