The Kolmogorov-Feller equation and the probabilistic model of quantum mechanics

Andrei Yu. Khrennikov

Oleg Georgievich Smolyanov, Andrei Yu. Khrennikov

Taku Matsui

Виктор Павлович Маслов

Calculations of probabilities are considered in the products of separable probability spaces, factored with respect to the permutation group of factors, by means of the trace operation with respect to the symmetric and antisymmetric orthonormal bases. A nonlinear Kolmogorov--Feller type equation is deduced which is the image of the forward linear Kolmogorov--Feller equation under factorization of the initial probability space with respect to the permutation group with certain rules of superselection.

Виктор Павлович Маслов

Andrei Yu. Khrennikov

The situation in probability theory is more or less analogous to the situation in geometry in the 19th century. Many scientists begin to understand that the Kol-mogorov axiomatic approach [1], 1933, to the modern theory of probability cannot describe all probabilistic phenomena observed in nature. Hence, the theory of probability based on this axiomatic approach is not a unique and universal probabilistic formalism. It is only one model, namely, the Kolmogorov probabilistic model. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.