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Spreading-invariant sequences and processes on bounded index sets
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  • Published: October 2000

Spreading-invariant sequences and processes on bounded index sets

  • Olav Kallenberg1 

Probability Theory and Related Fields volume 118, pages 211–250 (2000)Cite this article

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  • 5 Citations

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Abstract.

We say that a random sequence is spreadable if all subsequences of equal length have the same distribution. For infinite sequences the notion is equivalent to exchangeability but for finite sequences it is more general. The present paper is devoted to a systematic study of finite spreadable sequences and of processes on [0, 1] with spreadable increments. In particular, we show how many basic results in the exchangeable case—notably the predictable sampling theorem, the Wald-type identities, and various martingale and weak convergence results—admit extensions to a spreadable setting. We also identify some additional conditions that ensure the exchangeability of a spreadable sequence or process.

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Authors and Affiliations

  1. Department of Mathematics, Auburn University, 218 Parker Hall, Auburn, AL 36849-5310, USA. e-mail: olavk@mail.auburn.edu, , , , , , US

    Olav Kallenberg

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  1. Olav Kallenberg
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Additional information

Received: 9 November 1999 / Revised version: 16 March 2000 / Published online: 18 September 2000

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Cite this article

Kallenberg, O. Spreading-invariant sequences and processes on bounded index sets. Probab Theory Relat Fields 118, 211–250 (2000). https://doi.org/10.1007/s440-000-8015-x

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  • Issue Date: October 2000

  • DOI: https://doi.org/10.1007/s440-000-8015-x

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Keywords

  • Systematic Study
  • Additional Condition
  • Random Sequence
  • Weak Convergence
  • Convergence Result
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