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Exchangeability and Infinite Divisibility

In: The Fascination of Probability, Statistics and their Applications

Author

Listed:
  • Martin Drapatz

    (Ulm University, Institute for Mathematical Finance)

  • Alexander Lindner

    (Ulm University, Institute for Mathematical Finance)

Abstract

We characterize exchangeability of infinitely divisible distributions in terms of the characteristic triplet. This is applied to stable distributions and self-decomposable distributions, and a connection to Lévy copulas is made. We further study general mappings between classes of measures that preserve exchangeability and give various examples which arise from discrete time settings, such as stationary distributions of AR(1) processes, or from continuous time settings, such as Ornstein–Uhlenbeck processes or Upsilon-transforms.

Suggested Citation

  • Martin Drapatz & Alexander Lindner, 2016. "Exchangeability and Infinite Divisibility," Springer Books, in: Mark Podolskij & Robert Stelzer & Steen Thorbjørnsen & Almut E. D. Veraart (ed.), The Fascination of Probability, Statistics and their Applications, pages 99-126, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-25826-3_6
    DOI: 10.1007/978-3-319-25826-3_6
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