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Exchangeable random variables and the subsequence principle
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  • Published: September 1986

Exchangeable random variables and the subsequence principle

  • István Berkes1 &
  • Erika Péter2 

Probability Theory and Related Fields volume 73, pages 395–413 (1986)Cite this article

  • 168 Accesses

  • 13 Citations

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Summary

Call a sequence {X n } of r.v.'s ε-exchangeable if on the same probability space there exists an exchangeable sequence {Y n } such thatP(|X n −Y n |≧ε)≦ε for alln. We prove that any tight sequence {X n } defined on a rich enough probability space contains ε-exchangeable subsequences for every ε>0. The distribution of the approximating exchangeable sequences is also described in terms of {X n }. Our results give a convenient way to prove limit theorems for subsequences of general r.v. sequences. In particular, they provide a simplified way to prove the subsequence theorems of Aldous [1] and lead also to various extensions.

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Author information

Authors and Affiliations

  1. Mathematical Institute of the Hungarian Academy of Sciences, Reáltanoda u. 13-15, 1053, Budapest, Hungary

    István Berkes

  2. Department of Mathematics, Institute of Building, Dávid Ferenc u. 6, 1113, Budapest, Hungary

    Erika Péter

Authors
  1. István Berkes
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  2. Erika Péter
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Berkes, I., Péter, E. Exchangeable random variables and the subsequence principle. Probab. Th. Rel. Fields 73, 395–413 (1986). https://doi.org/10.1007/BF00776240

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  • Received: 28 December 1982

  • Revised: 04 October 1983

  • Accepted: 01 November 1985

  • Issue Date: September 1986

  • DOI: https://doi.org/10.1007/BF00776240

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Keywords

  • Stochastic Process
  • Probability Theory
  • Limit Theorem
  • Mathematical Biology
  • Probability Space
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