Review of Probability and Statistics

Vladimir I. Man’ko

A review of the new formulation of quantum mechanics in which the tomographic probability describes the quantum state instead of the wave function is presented. The tomographic probability in classical statistical mechanics is considered. The superposition principle is discussed.

Watanabe, Shinzo, Prokhorov, Jurii

Wolfgang Muckenheim, Günther Ludwig, Christopher Dewdney +6 more

Ole Eiler Barndorff-Nielsen, Richard David Gill, Peter E. Jupp

Summary Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems. Furthermore, developments in the theory of quantum measurements have brought the basic mathematical framework for the probability calculations much closer to that of classical probability theory. The present paper reviews this field and proposes and interrelates some new concepts for an extension of classical statistical inference to the quantum context.

Byron P. Roe

Andrei Yu. Khrennikov

This is a review about p‐adic valued probabilities, applications to quantum physics and cognitive sciences. We also do the next step in development of non‐Kolmogorovian models and consider an analogue of probability theory for probabilities taking values in topological groups. The main attention is paid to statistical interpretation of p‐adic probabilities as well as more general probabilities with values in topological groups.