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

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

$p$-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:

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} 

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

 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. 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
2. A. Yu. Khrennikov, “Laws of large numbers in non-Archimedean probability theory”, Izv. Math., 64:1 (2000), 207–219
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
4. Khrennikov A., Ludkovsky S., “Non-archimedean stochastic processes”, Ultrametric Functional Analysis, Contemporary Mathematics Series, 319, 2003, 139–157
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
6. E. I. Zelenov, “Models of $p$-adic mechanics”, Theoret. and Math. Phys., 174:2 (2013), 247–252
7. V. M. Maximov, “Multidimensional and abstract probability”, Proc. Steklov Inst. Math., 287:1 (2014), 174–201
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
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
•  Number of views: This page: 589 Full text: 160 References: 35 First page: 1