RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Guidelines for authors Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

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

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

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

Full text: PDF file (1707 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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
\Bibitem{KhrYam04} \by A.~Yu.~Khrennikov, Sh.~Yamada \paper On the concept of random sequence with respect to $p$-adic valued probabilities \jour Teor. Veroyatnost. i Primenen. \yr 2004 \vol 49 \issue 1 \pages 54--69 \mathnet{http://mi.mathnet.ru/tvp236} \crossref{https://doi.org/10.4213/tvp236} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2141330} \zmath{https://zbmath.org/?q=an:1090.60003} \transl \jour Theory Probab. Appl. \yr 2005 \vol 49 \issue 1 \pages 65--76 \crossref{https://doi.org/10.1137/S0040585X97980865} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000228185300004} 

• http://mi.mathnet.ru/eng/tvp236
• https://doi.org/10.4213/tvp236
• http://mi.mathnet.ru/eng/tvp/v49/i1/p54

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
•  Number of views: This page: 375 Full text: 118 References: 83