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Random arrays and functionals with multivariate rotational symmetries
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  • Published: March 1995

Random arrays and functionals with multivariate rotational symmetries

  • O. Kallenberg1 

Probability Theory and Related Fields volume 103, pages 91–141 (1995)Cite this article

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Summary

Our aim is to extend Schoenberg's classical theorem to higher dimensions, by establishing representations of arbitrary separately or jointly rotatable continuous linear random functionals in terms of multiple Wiener-Itô integrals and their tensor products. This leads to similar representations for separately or jointly rotatable arrays, and for separately or jointly exchangeable or spreadable random sheets.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Auburn University, 228 Parker Hall, 36849-5310, Auburn, AL, USA

    O. Kallenberg

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  1. O. Kallenberg
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Additional information

Research supported by NSF Grant DMS-9103050

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Kallenberg, O. Random arrays and functionals with multivariate rotational symmetries. Probab. Th. Rel. Fields 103, 91–141 (1995). https://doi.org/10.1007/BF01199033

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  • Received: 31 August 1994

  • Revised: 12 April 1995

  • Issue Date: March 1995

  • DOI: https://doi.org/10.1007/BF01199033

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Mathematics subject classifications

  • 60B99
  • 60G09
  • 47A80
  • 60G15
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