A maximal 𝕃_{𝕡}-inequality for stationary sequences and its applications

DOI10.1090/S0002-9939-06-08488-7zbMath1107.60011OpenAlexW1666477976MaRDI QIDQ3420024

Wei-Biao Wu, Magda Peligrad, Sergey Utev

Publication date: 1 February 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-06-08488-7

zbMATH Keywords

Markov chainsinvariance principlemartingalestationary processmaximal inequalityBernoulli shiftsrenewal sequences

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Functional limit theorems; invariance principles (60F17)

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Cites Work

• Unnamed Item
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• Distribution function inequalities for martingales
• A new maximal inequality and invariance principle for stationary sequences
• New dependence coefficients. Examples and applications to statistics
• A probability inequality for linear combinations of bounded random variables
• Central limit theorems for additive functionals of Markov chains.
• On Hoeffding's inequalities.
• Maximal inequalities for partial sums of \(\rho\)-mixing sequences
• Asymptotic theory of weakly dependent stochastic processes
• On the functional central limit theorem for stationary processes
• A new covariance inequality and applications.
• Convergence rates of the strong law for stationary mixing sequences
• The Convergence of Moments in the Central Limit Theorem for ρ-Mixing Sequences of Random Variables
• A central limit theorem for iterated random functions
• Limit theorems for iterated random functions
• An Inequality in Probability Theory