Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples
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Publication:1951694
DOI10.1214/11-AOP694zbMath1274.60056arXiv1103.3242MaRDI QIDQ1951694
Magda Peligrad, Florence Merlevède
Publication date: 24 May 2013
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1103.3242
martingalemaximal inequalitystationary sequencesmoment inequalityRosenthal inequalityprojective conditions
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Cites Work
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- Rates of convergence in the central limit theorem for linear statistics of martingale differences
- Kernel estimation for time series: an asymptotic theory
- On the functional central limit theorem via martingale approximation
- A note on a maximal Bernstein inequality
- Sums of random variables with \(\phi\)-mixing
- An empirical central limit theorem for dependent sequences
- On martingale approximations
- Almost sure invariance principle for dynamical systems by spectral methods
- Moment inequalities for sums of dependent random variables under projective conditions
- Rates of convergence for minimal distances in the central limit theorem under projective criteria
- An application of Rosenthal's moment inequality to the strong law of large numbers
- Moment and probability bounds with quasi-superadditive structure for the maximum partial sum
- Distribution function inequalities for martingales
- Almost-sure results for a class of dependent random variables
- The functional central limit theorem for strongly mixing processes
- Inequalities for absolutely regular sequences: application to density estimation
- A new maximal inequality and invariance principle for stationary sequences
- New dependence coefficients. Examples and applications to statistics
- Martingale approximations for sums of stationary processes.
- Maximal inequalities for partial sums of \(\rho\)-mixing sequences
- Asymptotic theory of weakly dependent stochastic processes
- Best constants in martingale version of Rosenthal's inequality
- Strong invariance principles for dependent random variables
- On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables
- Weak dependence. With examples and applications.
- Bernstein inequality and moderate deviations under strong mixing conditions
- [https://portal.mardi4nfdi.de/wiki/Publication:3048064 Estimation des densit�s: risque minimax]
- Convergence rates of the strong law for stationary mixing sequences
- A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION
- Some Limit Theorems for Random Functions. I
- A maximal 𝕃_{𝕡}-inequality for stationary sequences and its applications
- Some unbounded functions of intermittent maps for which the central limit theorem holds
- Exponential inequalities and functional central limit theorems for random fields
- STATIONARY ARCH MODELS: DEPENDENCE STRUCTURE AND CENTRAL LIMIT THEOREM
