RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 1993, Volume 97, Number 3, Pages 348–363 (Mi tmf1744)  

This article is cited in 9 scientific papers (total in 9 papers)

$p$-Adic probability theory and its applications. The principle of statistical stabilization of frequencies

A. Yu. Khrennikov

Moscow State Institute of Electronic Technology (Technical University)

Abstract: The development of $p$-adic quantum mechanics has made it necessary to construct a probability theory in which the probabilities of events are $p$-adic numbers. The foundations of this theory are developed here. The frequency definition of probability is used. A general principle of statistical stabilization of relative frequencies is formulated. By virtue of this principle, statistical stabilization of relative frequencies, which are, like all experimental data, rational numbers, can be considered not only in the real topology but also inp-adic topologies.

Full text: PDF file (1638 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 1993, 97:3, 1340–1348

Bibliographic databases:

Received: 23.11.1992

Citation: A. Yu. Khrennikov, “$p$-Adic probability theory and its applications. The principle of statistical stabilization of frequencies”, TMF, 97:3 (1993), 348–363; Theoret. and Math. Phys., 97:3 (1993), 1340–1348

Citation in format AMSBIB
\Bibitem{Khr93}
\by A.~Yu.~Khrennikov
\paper $p$-Adic probability theory and its applications. The principle of statistical stabilization of frequencies
\jour TMF
\yr 1993
\vol 97
\issue 3
\pages 348--363
\mathnet{http://mi.mathnet.ru/tmf1744}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1257875}
\zmath{https://zbmath.org/?q=an:0839.60005}
\transl
\jour Theoret. and Math. Phys.
\yr 1993
\vol 97
\issue 3
\pages 1340--1348
\crossref{https://doi.org/10.1007/BF01015763}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993NL72600003}


Linking options:
  • http://mi.mathnet.ru/eng/tmf1744
  • http://mi.mathnet.ru/eng/tmf/v97/i3/p348

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. S. A. Albeverio, P. E. Kloeden, A. Yu. Khrennikov, “Human memory as a $p$-adic dynamic system”, Theoret. and Math. Phys., 117:3 (1998), 1414–1422  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. Yu. Khrennikov, “Laws of large numbers in non-Archimedean probability theory”, Izv. Math., 64:1 (2000), 207–219  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. N. N. Ganikhodzhaev, F. M. Mukhamedov, U. A. Rozikov, “$\mathbb {Z}$Existence of a Phase Transition for the Potts $p$-adic Model on the Set $\mathbb {Z}$”, Theoret. and Math. Phys., 130:3 (2002), 425–431  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Khrennikov A., Ludkovsky S., “Non-archimedean stochastic processes”, Ultrametric Functional Analysis, Contemporary Mathematics Series, 319, 2003, 139–157  crossref  isi
    5. 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  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. E. I. Zelenov, “Models of $p$-adic mechanics”, Theoret. and Math. Phys., 174:2 (2013), 247–252  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. V. M. Maximov, “Multidimensional and abstract probability”, Proc. Steklov Inst. Math., 287:1 (2014), 174–201  mathnet  crossref  crossref  isi  elib  elib
    8. Rachid S., “Stable Random Field With P-Adic-Time and Spectral Density Estimation”, 2015 International Conference on Electrical and Electronics: Techniques and Applications (Eeta 2015), Destech Publications, Inc, 2015, 273–279  isi
    9. Ahmad Mohd Ali Khameini Liao L. Saburov M., “Periodic P-Adic Gibbs Measures of Q-State Potts Model on Cayley Trees i: the Chaos Implies the Vastness of the Set of P-Adic Gibbs Measures”, J. Stat. Phys., 171:6 (2018), 1000–1034  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:565
    Full text:154
    References:33
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019