Interpretations of Probability

Like geometry, probability can not be reduced to just one model to describe all physical and biological phenomena. Each model has a restricted range of applications. Quantum physics demonstrated that the use of conventional probability models induces some paradoxes. Such paradoxes can be resolved by using non-Kolmogorov probability models, developed on the basis of purely classical interpretations of probability: frequency and ensemble. Frequency models describe violations of the law of large numbers. Ensemble models are models with infinitely small probabilities.;This is the first fundamental book devoted to non-Kolomogorov probability models. It provides the first mathematical theory of negative probabilities - with numerous applications to quantum physics, information theory, complexity, biology and psychology. Natural models with negative (frequency and ensemble) probabilities are developed in the framework of so-called "p"-adic analysis. The book also contains an extremely interesting model of cognitive information reality with flows of information probabilities, describing the process of thinking, social and psychological phenomena.;This book should be of interest to specialists in probability theory, statistics, functional analysis, quantum physics and (partly) specialists in cognitive sciences and psychology.