Gaussian stationary processes: Adaptive wavelet decompositions, discrete approximations, and their convergence

DOI10.1007/s00041-008-9012-6zbMath1157.60028OpenAlexW1982932881MaRDI QIDQ2483007

Gustavo Didier, Vladas Pipiras

Publication date: 5 May 2008

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-008-9012-6

zbMATH Keywords

waveletssimulationARMA time seriesGaussian statonary processesprocesses with rational spectral densities

Mathematics Subject Classification ID

Gaussian processes (60G15) Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Stationary stochastic processes (60G10)

Related Items (13)

Properties of Some Random Series ⋮ Uniform Convergence of Wavelet Expansions of Gaussian Random Processes ⋮ On the vaguelet and Riesz properties of \(L^2\)-unbounded transformations of orthogonal wavelet bases ⋮ Adaptive wavelet decompositions of stationary time series ⋮ Statistical challenges in microrheology ⋮ Fourier series and Fourier–Haar series for stochastic measures ⋮ Fourier Series Expansion of Stochastic Measures ⋮ On the wavelet-based simulation of anomalous diffusion ⋮ Simulation of sub-Gaussian processes using wavelets ⋮ Wavelet-based simulation of random processes from certain classes with given accuracy and reliability ⋮ Convergence in \(L_{p}([0, T)\) of wavelet expansions of \(\varphi\)-sub-Gaussian random processes] ⋮ Convergence Rate of Wavelet Expansions of Gaussian Random Processes ⋮ Uniform Convergence of Compactly Supported Wavelet Expansions of Gaussian Random Processes

Cites Work

• Time series: theory and methods.
• Integration questions related to fractional Brownian motion
• Wavelet-type expansion of the Rosenblatt process
• Wavelets, generalized white noise and fractional integration: The synthesis of fractional Brownian motion
• Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition
• Wavelet-based simulation of fractional Brownian motion revisited
• Ten Lectures on Wavelets
• Wavelet approximation of deterministic and random signals: convergence properties and rates
• Adaptive wavelet decompositions of stationary time series
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