VARIANCE BOUNDING MARKOV CHAINS, L2-UNIFORM MEAN ERGODICITY AND THE CLT

DOI10.1142/S0219493711003176zbMath1210.60026OpenAlexW2128541173MaRDI QIDQ3083431

Michael Lin, Yves Derriennic

Publication date: 21 March 2011

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219493711003176

zbMATH Keywords

Markov chainscentral limit theoremuniform mean ergodicityvariance bounding

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Discrete-time Markov processes on general state spaces (60J05) Ergodic theory of linear operators (47A35)

Related Items (3)

Limit theorems for Markov chains by the symmetrization method ⋮ Almost everywhere convergence of convolution powers on compact Abelian groups ⋮ Randomized multivariate central limit theorems for ergodic homogeneous random fields

Cites Work

• Unnamed Item
• Unnamed Item
• Pointwise ergodic theorems with rate and application to the CLT for Markov chains
• Variance bounding Markov chains
• On variance conditions for Markov chain CLTs
• Stationary strongly mixing sequences not satisfying the central limit theorem
• Information regularity and the central limit question
• On the central limit question under absolute regularity
• Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions
• Refinements of the central limit theorem for a homogeneous Markov chain
• Quasi-compactness and uniform ergodicity of positive operators
• Geometric ergodicity and hybrid Markov chains
• A new maximal inequality and invariance principle for stationary sequences
• On the central limit theorem for geometrically ergodic Markov chains
• Acknowledgement of priority concerning ``On the central limit theorem for geometrically ergodic Markov chains
• A note on a variation of Doeblin's condition for uniform ergodicity of Markov chains
• Some aspects of recent works on limit theorems in ergodic theory with special emphasis on the ``central limit theorem
• Sets of multiplicity in locally compact abelian groups
• POINTWISE ERGODIC THEOREMS WITH RATE WITH APPLICATIONS TO LIMIT THEOREMS FOR STATIONARY PROCESSES
• Mixing Conditions for Markov Chains
• Speed of convergence of the n-fold convolution of a probability measure on a compact group
• Fourier-Stieltjes Transforms and Singular Infinite Convolutions
• On Singular Distributions
• Fractional Poisson equations and ergodic theorems for fractional coboundaries

This page was built for publication: VARIANCE BOUNDING MARKOV CHAINS, L₂-UNIFORM MEAN ERGODICITY AND THE CLT