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Semigroups of Upsilon transformations

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  • Barndorff-Nielsen, Ole E.
  • Maejima, Makoto

Abstract

Upsilon transformations satisfying certain regularity conditions are shown to generate semigroups of such transformations. This is based on a general commutativity property of the Upsilon transformations, and uses log infinite divisibility. The existence of random integral representations of Upsilon transformations and of the generated semigroups is also discussed.

Suggested Citation

  • Barndorff-Nielsen, Ole E. & Maejima, Makoto, 2008. "Semigroups of Upsilon transformations," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2334-2343, December.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:12:p:2334-2343
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    References listed on IDEAS

    as
    1. Ole E. Barndorff‐Nielsen & Alexander M. Lindner, 2007. "Lévy Copulas: Dynamics and Transforms of Upsilon Type," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(2), pages 298-316, June.
    2. Sato, Ken-iti & Yamazato, Makoto, 1984. "Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type," Stochastic Processes and their Applications, Elsevier, vol. 17(1), pages 73-100, May.
    3. Barndorff-Nielsen, Ole E. & Thorbjørnsen, Steen, 2006. "Regularizing mappings of Lévy measures," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 423-446, March.
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