The measure-theoretical approach to -adic probability theory
Andrei Khrennikov; Shinichi Yamada; Arnoud van Rooij
Annales mathématiques Blaise Pascal (1999)
- Volume: 6, Issue: 1, page 21-32
- ISSN: 1259-1734
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topKhrennikov, Andrei, Yamada, Shinichi, and van Rooij, Arnoud. "The measure-theoretical approach to $p$-adic probability theory." Annales mathématiques Blaise Pascal 6.1 (1999): 21-32. <http://eudml.org/doc/79205>.
@article{Khrennikov1999,
author = {Khrennikov, Andrei, Yamada, Shinichi, van Rooij, Arnoud},
journal = {Annales mathématiques Blaise Pascal},
keywords = {-adic probability formalism; -adic numbers; non-Archimedean measures; formula of the change of variables; conditional expectations for -adic valued random variables},
language = {eng},
number = {1},
pages = {21-32},
publisher = {Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal},
title = {The measure-theoretical approach to $p$-adic probability theory},
url = {http://eudml.org/doc/79205},
volume = {6},
year = {1999},
}
TY - JOUR
AU - Khrennikov, Andrei
AU - Yamada, Shinichi
AU - van Rooij, Arnoud
TI - The measure-theoretical approach to $p$-adic probability theory
JO - Annales mathématiques Blaise Pascal
PY - 1999
PB - Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
VL - 6
IS - 1
SP - 21
EP - 32
LA - eng
KW - -adic probability formalism; -adic numbers; non-Archimedean measures; formula of the change of variables; conditional expectations for -adic valued random variables
UR - http://eudml.org/doc/79205
ER -
References
top- 1. Albeverio, S., Khrennikov, A.Yu. - Representation of the Weyl group in spaces of square integrable functions with respect to p-adic valued Gaussian distributions. J. of Phys. A, 29, 5515-5527 (1996). Zbl0903.46073MR1419037
- 2. Albeverio, S., Khrennikov, A. Yu . - p-adic Hilbert space representation of quantum systems with an infinite number of degrees of freedom. Int. J. of Modern Phys., 10, No.13/14, 1665-1673 (1996). Zbl1229.81283MR1405192
- 3. Albeverio, S., Karwowski, W., A random walk on p-adics - the generator and its spectrum. Stochastic Process Appl., 53, 1 - 22 (1994). Zbl0810.60065MR1290704
- 4. Albeverio, S., Cianci, R., De Grande - De Kimpe, N., Khrennikov., A., p-adic theory of probability and foundations of quantum mechanics. Accepted for the publication in Russian J. of Math. Phys. Zbl1059.81503
- 5. Cramer, H. - Mathematical theory of statistics. Univ. Press, Princeton (1949).
- 6. Frampton, P. H.and Okada, Y. - p-adic string N-point function. Phys. Rev. Lett. B , 60, 484-486 (1988). MR925747
- 7. Frechet, M. - Recherches théoriques modernes sur la théorie des probabilités, Univ. Press., Paris (1937-1938). Zbl0015.26003JFM64.0536.01
- 8. Khrennikov, A.Yu. - p-adic valued distributions in mathematical physics. Kluwer Academic Publishers, Dordrecht (1994). Zbl0833.46061MR1325924
- 9. Khrennikov, A.Yu. - p-adic probability interpretation of Bell's inequality paradoxes. Physics Letters A, 200, 119-223 (1995). Zbl0910.60001MR1328131
- 10. Khrennikov, A.Yu. - p-adic probability distribution of hidden variables. Physica A, 215, 577-587 (1995).
- 11. Khrennikov, A.Yu. - p-adic theory of probability and its applications. A principle of the statistical stabilization of frequencies. Teor. and Matem. Fiz., 97, No. 3, 348-363 (1993). Zbl0839.60005MR1257875
- 12. Khrennikov, A.Yu. - Mathematical methods of the non-Archimedean physics. Uspekhi Mat. Nauk, 45, No. 4, 79-110 (1990). Zbl0722.46040MR1075387
- 13. Khrennikov, A.Yu. - Non-Archimedean analysis: quantum paradoxes, dynamical systems and biological models. Kluwer Academic Publishers, Dordrecht (1997). Zbl0920.11087MR1746953
- 14. Kolmogorov, A.N. - Foundations of the Probability Theory. Chelsea Publ. Comp., New York (1956). Zbl0074.12202MR79843
- 15. Mises, R.von , - The mathematical theory of probability and statistics. Academic, London(1964). Zbl0132.12303
- 16. Mises, R.von - Probability, Statistics and Truth. Macmillan, London (1957). MR90158
- 17. Monna, A. and Springer, T. - Integration non-Archimedienne, 1,2. Indag. Math., 25, 634-653(1963). Zbl0147.11803MR156936
- 18. Schikhov, W. - Ultrametric calculus. Cambridge Univ. Press, Cambridge (1984) Zbl0553.26006
- 19. Van Rooij, A. - Non-archimedean functional analysis. Marcel Dekker, Inc., New York (1978). Zbl0396.46061MR512894
- 20. Volovich, I.V. - p-adic string. Class. Quant. Grav.4, 83-87 (1987). MR895889
- 21. Vladimirov, V.S.and Volovich, I.V. - p-adic quantum mechanics. Commun. Math. Phys., 123, 659-676 (1989). Zbl0688.22004MR1006299
- 22. Vladimirov, V.S., Volovich, I.V., and Zelenov, E.I. - p-adic analysis and Mathematical Physics. World Scientific Publ., Singapure (1994). Zbl0812.46076MR1288093
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