On the weak invariance principle for stationary sequences under projective criteria

DOI10.1007/s10959-006-0029-yzbMath1117.60022OpenAlexW2124108320MaRDI QIDQ867084

Magda Peligrad, Florence Merlevède

Publication date: 14 February 2007

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10959-006-0029-y

zbMATH Keywords

weak invariance principlecentral limit theoremstrong mixing sequencesmartingale approximationprojective criteria

Mathematics Subject Classification ID

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

Related Items (16)

On the functional CLT for stationary Markov chains started at a point ⋮ Strong approximation for \(\rho \)-mixing sequences ⋮ Invariance principles for linear processes with application to isotonic regression ⋮ On the functional central limit theorem via martingale approximation ⋮ On martingale approximations and the quenched weak invariance principle ⋮ Almost sure invariance principles via martingale approximation ⋮ Strong approximation of partial sums under dependence conditions with application to dynamical systems ⋮ An invariance principle for fractional Brownian sheets ⋮ Strong invariance principles for dependent random variables ⋮ On the Komlós, Major and Tusnády strong approximation for some classes of random iterates ⋮ On the weak invariance principle for non-adapted sequences under projective criteria ⋮ Weakly dependent chains with infinite memory ⋮ A Central Limit Theorem for Reversible Processes with Nonlinear Growth of Variance ⋮ Asymptotic Properties for Linear Processes of Functionals of Reversible or Normal Markov Chains ⋮ Asymptotic for LS estimators in the EV regression model for dependent errors ⋮ Quenched Invariance Principles via Martingale Approximation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Ibragimov-Iosifescu conjecture for \(\phi\)-mixing sequences
• Central limit theorems for mixing sequences of random variables under minimal conditions
• Invariance principles for mixing sequences of random variables
• A maximal inequality and dependent strong laws
• On mixing and stability of limit theorems
• Almost sure invariance principles for mixing sequences of random variables
• On quantiles and the central limit question for strongly mixing sequences
• On the central limit theorem and its weak invariance principle for strongly mixing sequences with values in a Hilbert space via martingale approximation
• A new maximal inequality and invariance principle for stationary sequences
• Necessary and sufficient conditions for the conditional central limit theorem
• Central limit theorems for additive functionals of Markov chains.
• The functional central limit theorem under the strong mixing condition
• Martingale approximations for sums of stationary processes.
• On the functional central limit theorem for stationary processes
• A new covariance inequality and applications.
• A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION
• The invariance principle for ϕ-mixing sequences
• Moment inequalities and the strong laws of large numbers
• A Note on the Central Limit Theorems for Dependent Random Variables
• Invariance principles for dependent variables

This page was built for publication: On the weak invariance principle for stationary sequences under projective criteria