Relative entropy under mappings by stochastic matrices

DOI10.1016/0024-3795(93)90331-HzbMath0764.60068WikidataQ57065615 ScholiaQ57065615MaRDI QIDQ1208313

Joel E. Cohen, Yoh Iwasa, Mary Beth Ruskai, Gh. Rautu, Eugene Seneta, Gheorghe H. Zbăganu

Publication date: 16 May 1993

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Markov chainsrelative entropycontraction coefficientDobrushin's coefficient of ergodicity

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

Related Items (22)

About relaxation time of finite generalized Metropolis algorithms ⋮ A few remarks on asymptotic stabilities of Markov operators on \(L^1 \)-spaces ⋮ Equivalence of certain entropy contraction coefficients ⋮ \textit{Maxallent}: maximizers of all entropies and uncertainty of uncertainty ⋮ Ergodic properties of nonhomogeneous Markov chains defined on ordered Banach spaces with a base ⋮ Generalized Dobrushin ergodicity coefficient and uniform ergodicities of Markov operators ⋮ Weak ergodicity of nonhomogeneous Markov chains on noncommutative \(L^1\)-spaces ⋮ Uniform ergodicities of Markov semigroups on abstract states spaces ⋮ Universal Lyapunov functions for non-linear reaction networks ⋮ Entropy: the Markov ordering approach ⋮ Dependence of dissipation on the initial distribution over states ⋮ The Dobrushin ergodicity coefficient and the ergodicity of noncommutative Markov chains ⋮ Unnamed Item ⋮ Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory ⋮ Contraction coefficients for noisy quantum channels ⋮ Uniform ergodicities and perturbation bounds of Markov chains on base norm spaces ⋮ A Second Law for Open Markov Processes ⋮ Stability estimates of Markov semigroups on abstract states spaces ⋮ Contraction of Generalized Relative Entropy Under Stochastic Mappings on Matrices ⋮ Comparison of contraction coefficients for \(f\)-divergences ⋮ Monotone Riemannian metrics and relative entropy on noncommutative probability spaces ⋮ Uniform stability and weak ergodicity of nonhomogeneous Markov chains defined on ordered Banach spaces with a base

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Mathematical Theory of Communication
• On the relative entropy
• Sufficient subalgebras and the relative entropy of states of a von Neumann algebra
• Quasi-entropies for finite quantum systems
• Non-negative matrices and Markov chains. 2nd ed
• Eigenvalue inequalities for products of matrix exponentials
• Spreading of sets in product spaces and hypercontraction of the Markov operator
• On the selection of measures of distance between probability distributions
• Abschätzungen für die Eigenwerte positiver linearer Operatoren
• Information Theory and Statistical Mechanics
• Relative Entropy Measures of Multivariate Dependence
• Some convexity and subadditivity properties of entropy
• Coefficients of ergodicity: structure and applications
• Markov Processes and the H-Theorem
• Convex Analysis
• On Information and Sufficiency

This page was built for publication: Relative entropy under mappings by stochastic matrices