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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Received: 9 November 1999 / Revised version: 16 March 2000 / Published online: 18 September 2000
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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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DOI: https://doi.org/10.1007/s440-000-8015-x