8 research outputs found
Generalized probabilities taking values in non-Archimedean fields and topological groups
We develop an analogue of probability theory for probabilities taking values
in topological groups. We generalize Kolmogorov's method of axiomatization of
probability theory: main distinguishing features of frequency probabilities are
taken as axioms in the measure-theoretic approach. We also present a review of
non-Kolmogorovian probabilistic models including models with negative, complex,
and -adic valued probabilities. The latter model is discussed in details.
The introduction of -adic (as well as more general non-Archimedean)
probabilities is one of the main motivations for consideration of generalized
probabilities taking values in topological groups which are distinct from the
field of real numbers. We discuss applications of non-Kolmogorovian models in
physics and cognitive sciences. An important part of this paper is devoted to
statistical interpretation of probabilities taking values in topological groups
(and in particular in non-Archimedean fields)
A REVIEW OF EXTENDED PROBABILITIES
Some results emerging from the formalism of quantum theory seem to indicate probabilities outside of the conventional range between 0 and 1. This article draws attention to arguments in favour of extended probalilites, reviews some approaches to a formal account and interpretation, and presents a collection of statements of distinguished scientists about this strange topic. © 1986