Different closed-form expressions for generalized entropy rates of Markov chains

DOI10.1007/s11009-018-9679-3zbMath1455.94080OpenAlexW2899508992MaRDI QIDQ2176380

Philippe Regnault, Valérie Girardin, Loïck Lhote

Publication date: 4 May 2020

Published in: Methodology and Computing in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11009-018-9679-3

zbMATH Keywords

ergodic Markov chainentropy rateentropy distributionquasi-limit distribution

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Positive matrices and their generalizations; cones of matrices (15B48) Positive linear operators and order-bounded operators (47B65) Measures of information, entropy (94A17)

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Uses Software

• R

Cites Work

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• A Mathematical Theory of Communication
• Escort distributions minimizing the Kullback-Leibler divergence for a large deviations principle and tests of entropy level
• An informational divergence geometry for stochastic matrices
• \((h,\Psi)\)-entropy differential metric
• Entropy maximization for Markov and semi-Markov processes
• Weighted closed form expressions based on escort distributions for Rényi entropy rates of Markov chains
• Dynamical sources in information theory: Fundamental intervals and word prefixes
• Asymptotic behavior of absorbing Markov chains conditional on nonabsorption for applications in conservation biology
• Non-negative matrices and Markov chains.
• Rescaling Entropy and Divergence Rates
• Maxentropic Markov chains (Corresp.)
• Population Dynamics and Random Genealogies
• Maximal Entropy of Markov Chains with Common Steady-State Probabilities
• The entropy of Markov trajectories
• Exact aggregation of absorbing Markov processes using the quasi-stationary distribution
• Renyi's divergence and entropy rates for finite alphabet Markov sources
• Random walks pertaining to a class of deterministic weighted graphs
• Computation and Estimation of Generalized Entropy Rates for Denumerable Markov Chains
• Randomized Shortest-Path Problems: Two Related Models
• On Quasi-Stationary distributions in absorbing discrete-time finite Markov chains
• Estimation of the Entropy Rate of a Countable Markov Chain
• On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states