Real Functions in Stochastic Dependence

Dušana Babicová; Roman Frič

doi:10.2478/tmmp-2019-0016

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Real Functions in Stochastic Dependence

Tatra Mountains Mathematical Publications

Volume 74 (2019): Issue 1 (December 2019)

By: Dušana Babicová and Roman Frič

Open Access

|Nov 2019

Abstract

In a fuzzified probability theory, random events are modeled by measurable functions into [0,1] and probability measures are replaced with probability integrals. The transition from Boolean two-valued logic to Lukasiewicz multivalued logic results in an upgraded probability theory in which we define and study asymmetrical stochastic dependence/independence and conditional probability based on stochastic channels and joint experiments so that the classical constructions follow as particular cases. Elementary categorical methods enable us to put the two theories into a perspective.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2019-0016 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 17 - 34

Submitted on: Dec 11, 2017

Published on: Nov 15, 2019

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

measurable function,

stochastic dependence,

fuzzy random event,

observable,

probability measure,

probability integral,

state map,

statistical map,

joint experiment,

asymmetrical independence

Related subjects:

Mathematics,

General mathematics

© 2019 Dušana Babicová, Roman Frič, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 74 (2019): Issue 1 (December 2019)