Large scale behavior of wavelet coefficients of non-linear subordinated processes with long memory

DOI10.1016/j.acha.2011.04.003zbMath1244.60044arXiv1006.2282OpenAlexW2163134608MaRDI QIDQ412400

Ciprian A. Tudor, Murad S. Taqqu, François Roueff, Marianne Clausel

Publication date: 4 May 2012

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.2282

zbMATH Keywords

long-range dependenceself-similar processesWiener chaoswavelet coefficientsHermite processes

Mathematics Subject Classification ID

Gaussian processes (60G15) Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Signal detection and filtering (aspects of stochastic processes) (60G35) Numerical methods for wavelets (65T60)

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Cites Work

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• A wavelet analysis of the Rosenblatt process: chaos expansion and estimation of the self-similarity parameter
• Regularization and integral representations of Hermite processes
• Central limit theorems for arrays of decimated linear processes
• Central limit theorems for non-linear functionals of Gaussian fields
• Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series
• Multiple Wiener-Ito integrals. With applications to limit theorems
• Log-periodogram regression of time series with long range dependence
• Gaussian semiparametric estimation of long range dependence
• Estimators of long-memory: Fourier versus wavelets
• Asymptotic normality of wavelet estimators of the memory parameter for linear processes
• The Malliavin Calculus and Related Topics
• On the Spectral Density of the Wavelet Coefficients of Long-Memory Time Series with Application to the Log-Regression Estimation of the Memory Parameter
• Stein's method meets Malliavin calculus: a short survey with new estimates
• CLT and other limit theorems for functionals of Gaussian processes
• Long-range Dependence: Revisiting Aggregation with Wavelets
• Non-central limit theorems for non-linear functional of Gaussian fields
• Wavelet analysis of long-range-dependent traffic
• Wavelet estimation of the long memory parameter for Hermite polynomial of Gaussian processes