Hausdorff dimension of the graph of the fractional Brownian sheet

DOI10.4171/RMI/394zbMath1057.60033OpenAlexW2026762452MaRDI QIDQ1884177

Antoine Ayache

Publication date: 25 October 2004

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/39715

zbMATH Keywords

fractional Brownian motionHausdorff dimensionpacking dimensionGaussian fieldsrandom wavelet series

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Sums of independent random variables; random walks (60G50) Sample path properties (60G17)

Related Items (11)

A Fourier formulation of the Frostman criterion for random graphs and its applications to wavelet series. ⋮ Operator scaling stable random fields ⋮ Sojourn time dimensions of fractional Brownian motion ⋮ Multiparameter multifractional Brownian motion: local nondeterminism and joint continuity of the local times ⋮ A useful result related with zeros of continuous compactly supported mother wavelets ⋮ Dimension results of multifractional Brownian sheets ⋮ On the construction of stochastic fields with prescribed regularity by wavelet expansions ⋮ Sample path properties of generalized random sheets with operator scaling ⋮ Linear fractional stable sheets: Wavelet expansion and sample path properties ⋮ Gaussian fields and Gaussian sheets with generalized Cauchy covariance structure ⋮ The hyperbolic wavelet transform: an efficient tool for multifractal analysis of anisotropic fields

Cites Work

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• Occupation densities
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• Fractional Brownian sheet
• Wavelets, generalized white noise and fractional integration: The synthesis of fractional Brownian motion
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• Rate optimality of wavelet series approximations of fractional Brownian motion
• Fractional Brownian Fields as Integrals of White Noise
• Points multiples des trajectoires de processus gaussiens
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