Convergence of Markov chains in information divergence

DOI10.1007/s10959-007-0133-7zbMath1169.60016OpenAlexW2058409688MaRDI QIDQ1014048

Peter Harremoës, Klaus Kähler Holst

Publication date: 24 April 2009

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

Full work available at URL: https://doi.org/10.1007/s10959-007-0133-7

zbMATH Keywords

Markov chainergodic theoremsinformation divergencereversible Markov chaindecreasing informationincreasing information

Mathematics Subject Classification ID

Strong limit theorems (60F15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Information theory (general) (94A15) Probability theory on linear topological spaces (60B11)

Related Items (4)

Maximum entropy on compact groups ⋮ The maximum entropy rate description of a thermodynamic system in a stationary non-equilibrium state ⋮ Information in Probability: Another Information-Theoretic Proof of a Finite de Finetti Theorem ⋮ Freezing phase transition in a fractal potential

Cites Work

• Sanov property, generalized I-projection and a conditional limit theorem
• Entropy and the central limit theorem
• I-divergence geometry of probability distributions and minimization problems
• Fisher information inequalities and the central limit theorem
• Information theory and the limit-theorem for Markov chains and processes with a countable infinity of states
• Passage to the Limit under the Information and Entropy Signs
• Entropy and the Law of Small Numbers
• Binomial and Poisson distributions as maximum entropy distributions
• Information projections revisited
• Solution of Shannon’s problem on the monotonicity of entropy
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