ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 60 Khrennikov, Andrei, Vaxjo University, Sweden: Non-Kolmogorov models with p-adic probabilities Kolmogorov’s probabilistic formalism has its natural domain of applications. Thus it would be interesting to present non-Kolmogorov models. To have connection with reality, we have to develop a mathematical theory in connection with some interpretation of probability. We develop non-Kolmogorov models based on p-adic numbers To obtain a p-adic extension of the frequency probability theory (via R. von Mises), we use the evident fact: relative frequencies ν_{N} = n/N always belong Q. Thus we can study their behaviour, not only for the real metric ρ_{R} on Q, but for other metrics; for example, for p-adic metrics ρ_{p}. We study p-adic analogues of collectives of R. von Mises. Reference: A. Yu. Khrennikov, p-adic valued distributions in mathematical physics. Kluwer Academic Publishers, Dordrecht (1994).