Publication: Boolean valued representation of random Sets and markov kernels with application to large deviations
Authors
Avilés López, Antonio
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Publisher
MDPI
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DOI
https://doi.org/10.3390/math8101848
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info:eu-repo/semantics/article
Description
© 2020 by the authors. This manuscript version is made available under the CC-BY 4.0 license http://creativecommons.org/licenses/by/4.0/. This document is the Published version of a Published Work that appeared in final form in Mathematics. To access the final edited and published work see https://doi.org/10.3390/math8101848
Abstract
We establish a connection between random set theory and Boolean valued analysis by showing that random Borel sets, random Borel functions, and Markov kernels are respectively represented by Borel sets, Borel functions, and Borel probability measures in a Boolean valued model. This enables a Boolean valued transfer principle to obtain random set analogues of available theorems. As an application, we establish a Boolean valued transfer principle for large deviations theory, which allows for the systematic interpretation of results in large deviations theory as versions for Markov kernels. By means of this method, we prove versions of Varadhan and Bryc theorems, and a conditional version of Cramér theorem.
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Citation
Mathematics 2020, 8, 1848
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