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 Teor. Veroyatnost. i Primenen., 1995, Volume 40, Issue 2, Pages 458–464 (Mi tvp3493)

Short Communications

On the extension of the von mises frequency approach and Kolmogorov axiomatic approach to the $p$-adic probability theory

A. Yu. Khrennikov

Moscow State Institute of Electronic Technology (Technical University)

Abstract: The paper considers probabilistic models in which relative frequencies are stabilized in $p$-adic metric. The analog of frequency theory of von Mises probabilities is constructed for such models. As in usual probability theory, the properties of $p$-adic frequency probability are used to formulate the theory on an axiomatic level (the analog of the Kolmogorov axiomatic).

Keywords: rational and $p$-adic numbers, frequencies, statistic stabilization, collection, $p$-adic valued measures

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English version:
Theory of Probability and its Applications, 1995, 40:2, 371–376

Bibliographic databases:

Revised: 07.10.1993

Citation: A. Yu. Khrennikov, “On the extension of the von mises frequency approach and Kolmogorov axiomatic approach to the $p$-adic probability theory”, Teor. Veroyatnost. i Primenen., 40:2 (1995), 458–464; Theory Probab. Appl., 40:2 (1995), 371–376

Citation in format AMSBIB
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\by A.~Yu.~Khrennikov
\paper On the extension of the von mises frequency approach and Kolmogorov axiomatic approach to the $p$-adic probability theory
\jour Teor. Veroyatnost. i Primenen.
\yr 1995
\vol 40
\issue 2
\pages 458--464
\mathnet{http://mi.mathnet.ru/tvp3493}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1346483}
\zmath{https://zbmath.org/?q=an:0852.60002|0840.60005}
\transl
\jour Theory Probab. Appl.
\yr 1995
\vol 40
\issue 2
\pages 371--376
\crossref{https://doi.org/10.1137/1140040}

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This publication is cited in the following articles:
1. A. Yu. Khrennikov, Sh. Yamada, “On the concept of random sequence with respect to $p$-adic valued probabilities”, Theory Probab. Appl., 49:1 (2005), 65–76
2. Khrennikov A., “p-adic probability theory and its generalizations”, p-ADIC Mathematical Physics, AIP Conference Proceedings, 826, 2006, 105–120
3. Khrennikov A.Yu., “Generalized probabilities taking values in non–Archimedean fields and in topological groups”, Russian Journal of Mathematical Physics, 14:2 (2007), 142–159
4. V. M. Maksimov, “Finite probabilistic structures”, Discrete Math. Appl., 18:4 (2008), 341–350
5. Perrin Y., “A Journey Throughout the History of P-Adic Numbers”, Advances in Ultrametric Analysis, Contemporary Mathematics, 704, eds. Escassut A., PerezGarcia C., Shamseddine K., Amer Mathematical Soc, 2018, 261–272
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