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Teor. Veroyatnost. i Primenen., 2004, Volume 49, Issue 1, Pages 54–69 (Mi tvp236)  

This article is cited in 1 scientific paper (total in 1 paper)

On the concept of random sequence with respect to $p$-adic valued probabilities

A. Yu. Khrennikova, Sh. Yamadab

a Växjö University
b University of Tokyo

Abstract: This paper continues investigations on generalized probability models in which probabilities belong to fields of $p$-adic numbers. We study a $p$-adic generalization of Martin–Löf's theory based on tests for randomness. Such generalization appears to be the most natural approach to $p$-adic randomness. Each test for randomness induces a series of limit theorems. We proved that it is possible to enumerate all $p$-adic tests for randomness. However, in contrast to Martin–Löf's theory for real probabilities we proved that a universal test for randomness does not exist.

Keywords: randomness, collective, Kolmogorov model, von Mises model, $p$-adic numbers.

DOI: https://doi.org/10.4213/tvp236

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English version:
Theory of Probability and its Applications, 2005, 49:1, 65–76

Bibliographic databases:

Received: 28.06.2000

Citation: A. Yu. Khrennikov, Sh. Yamada, “On the concept of random sequence with respect to $p$-adic valued probabilities”, Teor. Veroyatnost. i Primenen., 49:1 (2004), 54–69; Theory Probab. Appl., 49:1 (2005), 65–76

Citation in format AMSBIB
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\jour Theory Probab. Appl.
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\pages 65--76
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Mukhamedov F.M., Rozikov U.A., Mendes J.F.F., “On phase transitions for p-adic Potts model with competing interactions on a Cayley tree”, p-ADIC Mathematical Physics, AIP Conference Proceedings, 826, 2006, 140–150  crossref  mathscinet  zmath  adsnasa  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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