On the Komlós, Major and Tusnády strong approximation for some classes of random iterates

DOI10.1016/j.spa.2017.07.011zbMath1384.60071arXiv1706.08282OpenAlexW2727975411MaRDI QIDQ1743346

Florence Merlevède, Christophe Cuny, Jérôme Dedecker

Publication date: 13 April 2018

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.08282

zbMATH Keywords

Markov chainsstrong invariance principleKMT approximationleft random walk on \(G L_d(\mathbb{R})\)random iterates

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 (10)

Large deviation expansions for the coefficients of random walks on the general linear group ⋮ Random walks on \(\mathrm{SL}_2({\mathbb{C}})\): spectral gap and limit theorems ⋮ Berry-Esseen type bounds for the left random walk on \({\mathrm{GL}_d}(\mathbb{R})\) under polynomial moment conditions ⋮ Strong invariance principles for ergodic Markov processes ⋮ A Berry-Esseen bound with (almost) sharp dependence conditions ⋮ Rates of convergence in invariance principles for random walks on linear groups via martingale methods ⋮ Rates in almost sure invariance principle for slowly mixing dynamical systems ⋮ An alternative to the coupling of Berkes-Liu-Wu for strong approximations ⋮ Rates in almost sure invariance principle for quickly mixing dynamical systems ⋮ Sharp connections between Berry-Esseen characteristics and Edgeworth expansions for stationary processes

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