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Uniform Distributions on the Integers: A connection to the Bernouilli Random Walk

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  • Joseph B. Kadane
  • Jiashun Jin

Abstract

Associate to each subset of the integers its almost sure limiting relative frequency under the Bernouilli random walk, if it has one. The resulting probability space is purely finitely additive, and uniform in the sense of residue classes and shift-invariance. However, it is not uniform in the sense of limiting relative frequency.

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  • Joseph B. Kadane & Jiashun Jin, 2014. "Uniform Distributions on the Integers: A connection to the Bernouilli Random Walk," Econometric Reviews, Taylor & Francis Journals, vol. 33(1-4), pages 372-378, June.
    • Handle: RePEc:taf:emetrv:v:33:y:2014:i:1-4:p:372-378
    DOI: 10.1080/07474938.2013.807193
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    References listed on IDEAS

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    1. Rao, C. Radhakrishna & Shanbhag, D. N., 1991. "An elementary proof for an extended version of the Choquet-Deny theorem," Journal of Multivariate Analysis, Elsevier, vol. 38(1), pages 141-148, July.
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    Cited by:

    1. Pierre Druilhet & Erwan Saint Loubert Bié, 2021. "Improper versus finitely additive distributions as limits of countably additive probabilities," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1187-1202, December.

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