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Some new representations in bivariate exchangeability
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  • Published: March 1988

Some new representations in bivariate exchangeability

  • Olav Kallenberg1 

Probability Theory and Related Fields volume 77, pages 415–455 (1988)Cite this article

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Summary

Consider an array X = (X ij ,i,j∈N) of random variables, and let U=(U ij ) and V=(V ij ) be orthogonal transformations affecting only finitely many coordinates. Say that X is separately rotatable if \(UXV^T \mathop = \limits^d X\) for arbitrary U and V, and jointly rotatable if this holds with U=V. Restricting U and V to the class of permutations, we get instead the property of separate or joint exchangeability. Processes on ℝ 2+ , ℝ+ × [0,1] or [0, 1]2 are said to be separately or jointly exchangeable, if the arrays of increments over arbitrary square grids have these properties. For some of the above cases, explicit representations have recently been obtained, independently, by Aldous and Hoover. The aim of the present paper is to continue the work of these authors by deriving some new representations, and by solving the associated uniqueness and continuity problems.

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Authors and Affiliations

  1. Mathematics ACA, Auburn University, 120 Mathematics Annex, 36849-3501, Auburn, AL, USA

    Olav Kallenberg

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  1. Olav Kallenberg
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Additional information

Research suported by the Air Force Office of Scientific Research Grant No. F 49620 85C 0144

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Kallenberg, O. Some new representations in bivariate exchangeability. Probab. Th. Rel. Fields 77, 415–455 (1988). https://doi.org/10.1007/BF00319298

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  • Received: 29 July 1986

  • Revised: 10 October 1987

  • Issue Date: March 1988

  • DOI: https://doi.org/10.1007/BF00319298

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Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Explicit Representation
  • Orthogonal Transformation
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