On martingale approximations and the quenched weak invariance principle

DOI10.1214/13-AOP856zbMath1354.60031arXiv1202.2964MaRDI QIDQ2447340

Christophe Cuny, Florence Merlevède

Publication date: 25 April 2014

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.2964

zbMATH Keywords

ergodic theoremsstationary processmoderate deviationsquenched invariance principlemartingale approximationWasserstein distancesMarcinkiewicz-Zygmund theorem\(L^p\)-error

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10) Strong limit theorems (60F15) Large deviations (60F10) Functional limit theorems; invariance principles (60F17) (L^p)-limit theorems (60F25)

Related Items (20)

On the functional CLT for stationary Markov chains started at a point ⋮ Limit theorems and inequalities via martingale methods ⋮ Invariance principle via orthomartingale approximation ⋮ Self-normalized Cramér type moderate deviations for stationary sequences and applications ⋮ A quenched weak invariance principle ⋮ Functional central limit theorem via nonstationary projective conditions ⋮ On Rio's proof of limit theorems for dependent random fields ⋮ On the quenched CLT for stationary Markov chains ⋮ Ergodicity and central limit theorem for random interval homeomorphisms ⋮ On the quenched central limit theorem for stationary random fields under projective criteria ⋮ On the normal approximation for random fields via martingale methods ⋮ On the Komlós, Major and Tusnády strong approximation for some classes of random iterates ⋮ Hölderian weak invariance principle under the Maxwell and Woodroofe condition ⋮ CLT for random walks of commuting endomorphisms on compact abelian groups ⋮ Quenched limit theorems for Fourier transforms and periodogram ⋮ Cramér-type moderate deviations for stationary sequences of bounded random variables ⋮ Functional CLT for martingale-like nonstationary dependent structures ⋮ Quenched invariance principles for orthomartingale-like sequences ⋮ Limits theorems for random walks on homeo\(( \mathrm{S}^1)\) ⋮ Quenched Invariance Principles via Martingale Approximation

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