Exchangeability and Infinite Divisibility

Martin Drapatz () and Alexander Lindner ()
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Martin Drapatz: Ulm University, Institute for Mathematical Finance
Alexander Lindner: Ulm University, Institute for Mathematical Finance

A chapter in The Fascination of Probability, Statistics and their Applications, 2016, pp 99-126 from Springer

Abstract: 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.

Keywords: Exchangeability; Exchangeability preserving transformation; Infinitely divisible distribution; Lévy copula; Ornstein-Uhlenbeck process; Random recurrence equation; Upsilon-transform (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-25826-3_6

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DOI: 10.1007/978-3-319-25826-3_6

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