On the Functional Central Limit Theorem for Reversible Markov Chains with Nonlinear Growth of the Variance

DOI10.1239/jap/1354716659zbMath1269.60041arXiv1112.2751OpenAlexW2074041886MaRDI QIDQ4903044

Costel Peligrad, Martial Longla, Magda Peligrad

Publication date: 19 January 2013

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

Full work available at URL: https://arxiv.org/abs/1112.2751

zbMATH Keywords

functional central limit theoremMarkov chaintightnessmaximal inequalitymartingale approximationreversible process

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Discrete-time Markov processes on general state spaces (60J05) Functional limit theorems; invariance principles (60F17)

Related Items (4)

Frames and factorization of graph Laplacians ⋮ On the invariance principle for reversible Markov chains ⋮ Remarks on limit theorems for reversible Markov processes and their applications ⋮ Asymptotic Properties for Linear Processes of Functionals of Reversible or Normal Markov Chains

Cites Work

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• Moment inequalities for sums of dependent random variables under projective conditions
• Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions
• Forward-backward martingale decomposition and compactness results for additive functionals of stationary ergodic Markov processes
• The functional central limit theorem for strongly mixing processes
• Martingale approximations for sums of stationary processes.
• Markov chains for exploring posterior distributions. (With discussion)
• Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples
• Asymptotic theory of weakly dependent stochastic processes
• Central limit theorem started at a point for stationary processes and additive functionals of reversible Markov chains
• Law of the iterated logarithm for stationary processes
• A Central Limit Theorem for Reversible Processes with Nonlinear Growth of Variance
• The central limit theorem for Markov chains with normal transition operators, started at a point

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