Conditional Expectation in an Uncertainty Space

In the classical (probability) setting, the Radon-Nikodym Theorem is used to prove the existence of conditional expectations. This paper states the Radon-Nikodym Theorem for uncertain measures which were introduced by Liu (2007) to model belief degrees. This version of the theorem is adapted from Gr...

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Main Authors:	Aujero, E, Frondoza, M, De Lara-Tuprio, Elvira P, Eden, R, Teng, T R
Format:	text
Published:	Archīum Ateneo 2019
Subjects:	uncertainty theory conditional expectation Mathematics
Online Access:	https://archium.ateneo.edu/mathematics-faculty-pubs/69 https://iopscience.iop.org/article/10.1088/1742-6596/1180/1/012003/meta
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Institution:	Ateneo De Manila University

id	ph-ateneo-arc.mathematics-faculty-pubs-1068
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spelling	ph-ateneo-arc.mathematics-faculty-pubs-10682020-05-22T07:19:49Z Conditional Expectation in an Uncertainty Space Aujero, E Frondoza, M De Lara-Tuprio, Elvira P Eden, R Teng, T R In the classical (probability) setting, the Radon-Nikodym Theorem is used to prove the existence of conditional expectations. This paper states the Radon-Nikodym Theorem for uncertain measures which were introduced by Liu (2007) to model belief degrees. This version of the theorem is adapted from Graf (1980) who established the theorem for non-additive measures called capacities. This paper then uses the theorem to define the conditional expectation of an uncertain variable with respect to a σ-algebra. Properties of the conditional expectation are established. 2019-01-01T08:00:00Z text https://archium.ateneo.edu/mathematics-faculty-pubs/69 https://iopscience.iop.org/article/10.1088/1742-6596/1180/1/012003/meta Mathematics Faculty Publications Archīum Ateneo uncertainty theory conditional expectation Mathematics
institution	Ateneo De Manila University
building	Ateneo De Manila University Library
continent	Asia
country	Philippines Philippines
content_provider	Ateneo De Manila University Library
collection	archium.Ateneo Institutional Repository
topic	uncertainty theory conditional expectation Mathematics
spellingShingle	uncertainty theory conditional expectation Mathematics Aujero, E Frondoza, M De Lara-Tuprio, Elvira P Eden, R Teng, T R Conditional Expectation in an Uncertainty Space
description	In the classical (probability) setting, the Radon-Nikodym Theorem is used to prove the existence of conditional expectations. This paper states the Radon-Nikodym Theorem for uncertain measures which were introduced by Liu (2007) to model belief degrees. This version of the theorem is adapted from Graf (1980) who established the theorem for non-additive measures called capacities. This paper then uses the theorem to define the conditional expectation of an uncertain variable with respect to a σ-algebra. Properties of the conditional expectation are established.
format	text
author	Aujero, E Frondoza, M De Lara-Tuprio, Elvira P Eden, R Teng, T R
author_facet	Aujero, E Frondoza, M De Lara-Tuprio, Elvira P Eden, R Teng, T R
author_sort	Aujero, E
title	Conditional Expectation in an Uncertainty Space
title_short	Conditional Expectation in an Uncertainty Space
title_full	Conditional Expectation in an Uncertainty Space
title_fullStr	Conditional Expectation in an Uncertainty Space
title_full_unstemmed	Conditional Expectation in an Uncertainty Space
title_sort	conditional expectation in an uncertainty space
publisher	Archīum Ateneo
publishDate	2019
url	https://archium.ateneo.edu/mathematics-faculty-pubs/69 https://iopscience.iop.org/article/10.1088/1742-6596/1180/1/012003/meta
_version_	1722366472008761344

Conditional Expectation in an Uncertainty Space

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