Exact convergence rates in the central limit theorem for a class of martingales

DOI10.3150/07-BEJ6116zbMath1139.60309arXivmath/0403385MaRDI QIDQ2469662

Mohamed El Machkouri, Lahcen Ouchti

Publication date: 6 February 2008

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0403385

zbMATH Keywords

rate of convergencecentral limit theoremmartingale difference sequenceLindeberg's decomposition

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05)

Related Items (10)

On Wasserstein-1 distance in the central limit theorem for elephant random walk ⋮ On quantitative bounds in the mean martingale central limit theorem ⋮ Rates of convergence in the central limit theorem for martingales in the non stationary setting ⋮ A Berry-Esseen bound of order \(\frac{1}{\sqrt{n}}\) for martingales ⋮ Random matrices: law of the determinant ⋮ On the Wasserstein distance for a martingale central limit theorem ⋮ On the rate of convergence in the central limit theorem for arrays of random vectors ⋮ Exact rates of convergence in some martingale central limit theorems ⋮ Convergence rates in the central limit theorem for weighted sums of Bernoulli random fields ⋮ Cramér moderate deviations for the elephant random walk

Cites Work

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• A note on the rate of convergence in the martingale central limit theorem
• Exact convergence rates in some martingale central limit theorems
• Approximating martingales and the central limit theorem for strictly stationary processes
• On the rate of convergence in the central limit theorem for martingale difference sequences
• About the Berry-Esseen theorem for weakly dependent sequences
• Some Bounds on the Rate of Convergence in the CLT for Martingales. II
• The Berry-Esseen theorem for functionals of discrete Markov chains
• On the rate of convergence in the central limit theorem for Markov-chains
• Vitesse de convergence dans le TCL pour des chaı̂nes de Markov et certains processus associés à des systèmes dynamiques
• Some Bounds on the Rate of Convergence in the CLT for Martingales. I
• Vitesse dans le théorème limite central pour certains systèmes dynamiques quasi-hyperboliques
• The Remainder in the Central Limit Theorem for Mixing Stochastic Processes
• Martingale Central Limit Theorems
• ON THE CENTRAL AND LOCAL LIMIT THEOREM FOR MARTINGALE DIFFERENCE SEQUENCES
• A Central Limit Theorem for a Class of Dependent Random Variables
• The Accuracy of the Gaussian Approximation to the Sum of Independent Variates

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