On the functional central limit theorem via martingale approximation

DOI10.3150/10-BEJ276zbMath1284.60070arXiv0910.3448OpenAlexW3102972652MaRDI QIDQ637109

Magda Peligrad, Mikhaĭl Iosifovich Gordin

Publication date: 2 September 2011

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.3448

zbMATH Keywords

martingale approximationreversible Markov chainmixing sequencesconditional functional central limit theorem

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) 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 (15)

On the functional CLT for stationary Markov chains started at a point ⋮ Limit theorems and inequalities via martingale methods ⋮ Iterated invariance principle for slowly mixing dynamical systems ⋮ Randomization in the construction of multidimensional martingales ⋮ Invariance principle via orthomartingale approximation ⋮ Functional central limit theorem via nonstationary projective conditions ⋮ Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples ⋮ On martingale approximations and the quenched weak invariance principle ⋮ Almost sure invariance principles via martingale approximation ⋮ A functional CLT for fields of commuting transformations via martingale approximation ⋮ Closability, regularity, and approximation by graphs for separable bilinear forms ⋮ A Central Limit Theorem for Temporally Nonhomogenous Markov Chains with Applications to Dynamic Programming ⋮ Functional CLT for martingale-like nonstationary dependent structures ⋮ A Least Squares Estimator for Lévy-driven Moving Averages Based on Discrete Time Observations ⋮ Quenched Invariance Principles via Martingale Approximation

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