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 Teor. Veroyatnost. i Primenen., 1995, Volume 40, Issue 1, Pages 189–192 (Mi tvp3331)

Short Communications

On probability distributions on the field of $p$-adic numbers

A. Yu. Khrennikov

Moscow Electronic Engineering Institute

Abstract: It is shown that many naturally defined probability distributions can be realized as distributions on the field of $p$-adic numbers. Following R. Mises and E. Tornier we consider first the stochastic experiment whose elementary outcome is the result of the infinite sequence of tossings of a symmetric coin. It is proved that the distribution corresponding to this experiment is the Haar distribution on the ring of $p$-adic integers. Then we consider the convergence of series of random variables with rational values on the field of $p$-adic numbers. It is shown that the series converge a.s. on the field of $p$-adic numbers but diverge on the field of real numbers.

Keywords: Tornier distribution, $p$-adic numbers, Haar distribution.

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English version:
Theory of Probability and its Applications, 1995, 40:1, 159–162

Bibliographic databases:

Citation: A. Yu. Khrennikov, “On probability distributions on the field of $p$-adic numbers”, Teor. Veroyatnost. i Primenen., 40:1 (1995), 189–192; Theory Probab. Appl., 40:1 (1995), 159–162

Citation in format AMSBIB
\Bibitem{Khr95} \by A.~Yu.~Khrennikov \paper On probability distributions on the field of $p$-adic numbers \jour Teor. Veroyatnost. i Primenen. \yr 1995 \vol 40 \issue 1 \pages 189--192 \mathnet{http://mi.mathnet.ru/tvp3331} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1346743} \zmath{https://zbmath.org/?q=an:0848.60011} \transl \jour Theory Probab. Appl. \yr 1995 \vol 40 \issue 1 \pages 159--162 \crossref{https://doi.org/10.1137/1140014} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996UH07100014} 

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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. 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
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