Boolean Valued Representation of Random Sets and Markov Kernels with Application to Large Deviations

Antonio Avilés López and José Miguel Zapata García
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Antonio Avilés López: Departamento de Matematica, Universidad de Murcia, Espinardo, 30100 Murcia, Spain
José Miguel Zapata García: School of Mathematics and Statistics, University College Dublin, Belfield, 58622 Dublin 4, Ireland

Mathematics, 2020, vol. 8, issue 10, 1-23

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.

Keywords: Boolean valued analysis; random sets; Markov kernels; large deviations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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