Uniform CLT for Markov chains and its invariance principle: A martingale approach

DOI10.1007/BF02218044zbMath0865.60016MaRDI QIDQ1900163

Shlomo Levental, Jongsig Bae

Publication date: 7 July 1997

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

zbMATH Keywords

Markov chainsmartingalesinvariance principleuniform central limit theorem

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Functional limit theorems; invariance principles (60F17)

Related Items (7)

Weak convergence of some classes of martingales with jumps. ⋮ Nonparametric tests for conditional symmetry in dynamic models ⋮ Exponential concentration inequalities for additive functionals of Markov chains ⋮ Weak convergence of non-stationary multivariate marked processes with applications to martingale testing ⋮ Specification tests of parametric dynamic conditional quantiles ⋮ Unnamed Item ⋮ Donsker theorems for diffusions: necessary and sufficient conditions

Cites Work

• A central limit theorem under metric entropy with \(L_ 2\) bracketing
• On tail probabilities for martingales
• Invariance principles for absolutely regular empirical processes
• The central limit theorem for stochastic processes
• A uniform CLT for uniformly bounded families of martingale differences
• Invariance principles for sums of Banach space valued random elements and empirical processes
• Convergence of stochastic processes
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