RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
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



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 3, Pages 207–223 (Mi izv27)  

A limit theorem for $p$-adic-valued probability distributions

A. Yu. Khrennikov


Abstract: Probability models in which probabilities, defined in the sense of von Mises as limits of relative frequencies, can belong to $p$-adic number fields appeared in connection with the problem of the probabilistic interpretation of wave functions in $p$-adic-valued quantum mechanics and field theory. Here we present a variant of axiomatic $p$-adic probability theory in the framework of the theory of analytic distributions on $p$-adic spaces. We prove a theorem on the existence of $p$-adic-valued probability distributions on $p$-adic sequences and obtain a limit theorem for sums of independent random variables (an analogue of the law of large numbers).

Full text: PDF file (1592 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 1995, 59:3, 647–662

Bibliographic databases:

MSC: 60A05
Received: 13.05.1993

Citation: A. Yu. Khrennikov, “A limit theorem for $p$-adic-valued probability distributions”, Izv. RAN. Ser. Mat., 59:3 (1995), 207–223; Izv. Math., 59:3 (1995), 647–662

Citation in format AMSBIB
\Bibitem{Khr95}
\by A.~Yu.~Khrennikov
\paper A~limit theorem for $p$-adic-valued probability distributions
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 3
\pages 207--223
\mathnet{http://mi.mathnet.ru/izv27}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1347083}
\zmath{https://zbmath.org/?q=an:0898.60005}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 3
\pages 647--662
\crossref{https://doi.org/10.1070/IM1995v059n03ABEH000027}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995TJ19700008}


Linking options:
  • http://mi.mathnet.ru/eng/izv27
  • http://mi.mathnet.ru/eng/izv/v59/i3/p207

    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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:281
    Full text:70
    References:46
    First page:1

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