Sup-sums principles for \(F\)-divergence and a new definition for \(t\)-entropy

DOI10.1007/s10959-020-01046-5zbMath1501.26012OpenAlexW3096530532MaRDI QIDQ2116482

A. V. Lebedev, Victor Bakhtin

Publication date: 17 March 2022

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10959-020-01046-5

zbMATH Keywords

Kullback-Leibler divergencepartition of unity\(F\)-divergence\(t\)-entropysup-sums principle

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) Inequalities for sums, series and integrals (26D15) Measures of information, entropy (94A17) Convexity of real functions in one variable, generalizations (26A51)

Cites Work

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• Large deviations for bootstrapped empirical measures
• Legendre analysis, thermodynamic formalism, and spectra of Perron-Frobenius operators
• Parametric estimation and tests through divergences and the duality technique
• A sandwich proof of the Shannon-McMillan-Breiman theorem
• A Cramér type theorem for weighted random variables
• On the f-divergence and singularity of probability measures
• A road to the spectral radius of transfer operators
• Entropy and variational principle for one-dimensional lattice systems with a generala prioriprobability: positive and zero temperature
• Ont-entropy and variational principle for the spectral radii of transfer and weighted shift operators
• On t-entropy and variational principle for the spectral radius of weighted shift operators
• Minimization of φ-divergences on sets of signed measures
• On Divergences and Informations in Statistics and Information Theory
• A Variational Principle for the Pressure of Continuous Transformations
• Statistical Mechanics on a Compact Set with Z p Action Satisfying Expansiveness and Specification
• A Weighted Bootstrap Procedure for Divergence Minimization Problems
• Markov Processes and the H-Theorem
• The Basic Theorems of Information Theory

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