<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

Real Functions in Stochastic Dependence

Mathematical Institute, Slovak Academy of Sciences

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Real Functions in Stochastic Dependence"}

In a fuzzified probability theory, random events are modeled by measurable functions into [0,1] and probability measures are replaced with probability...

Real Functions in Stochastic Dependence

Published Online: Nov 15, 2019

Page range: 17 - 34

Received: Dec 11, 2017

DOI: https://doi.org/10.2478/tmmp-2019-0016

Keywords
measurable function, stochastic dependence, fuzzy random event, observable, probability measure, probability integral, state map, statistical map, joint experiment, asymmetrical independence

© 2019 Dušana Babicová et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Real Functions in Stochastic Dependence

Published Online: Nov 15, 2019

Page range: 17 - 34

Received: Dec 11, 2017

DOI: https://doi.org/10.2478/tmmp-2019-0016

Keywordsmeasurable function, stochastic dependence, fuzzy random event, observable, probability measure, probability integral, state map, statistical map, joint experiment, asymmetrical independence

© 2019 Dušana Babicová et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
measurable function, stochastic dependence, fuzzy random event, observable, probability measure, probability integral, state map, statistical map, joint experiment, asymmetrical independence