A Proof of Sanov’s Theorem via Discretizations

Rangel Baldasso (), Roberto I. Oliveira (), Alan Pereira () and Guilherme Reis ()
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Rangel Baldasso: Leiden University
Roberto I. Oliveira: IMPA
Alan Pereira: Universidade Federal de Alagoas
Guilherme Reis: Technische Universität München

Journal of Theoretical Probability, 2023, vol. 36, issue 1, 646-660

Abstract: Abstract We present an alternative proof of Sanov’s theorem for Polish spaces in the weak topology that follows via discretization arguments. We combine the simpler version of Sanov’s theorem for discrete finite spaces and well-chosen finite discretizations of the Polish space. The main tool in our proof is an explicit control on the rate of convergence for the approximated measures.

Keywords: Large deviations; Sanov’s Theorem; 60F10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01174-0

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