Fractional differentiation in the self-affine case. IV — random measures

DOI10.1080/17442509408833912zbMath0827.60035OpenAlexW2031234673MaRDI QIDQ4849122

Norbert Patzschke, Martina Zähle

Publication date: 26 November 1995

Published in: Stochastics and Stochastic Reports (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17442509408833912

zbMATH Keywords

self-similarityrandom measuresself-affinityconcept of fractional differentiation of stochastic processesfractional densities

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Random measures (60G57) Fractals (28A80)

Related Items (4)

ON THE FRACTIONAL DERIVATIVE OF A TYPE OF SELF-AFFINE CURVES ⋮ Riesz s-equilibrium measures on \(d\)-dimensional fractal sets as \(s\) approaches \(d\) ⋮ The average density of the path of planar Brownian motion ⋮ Some Random sequences related to average density of self-similar measures

Cites Work

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• Statistically self-similar fractals
• Self-similar random measures. I: Notion, carrying Hausdorff dimension, and hyperbolic distribution
• Occupation densities
• Fractional differentiation in the self-affine case. I: Random functions
• Wavelet transforms and order-two densities of fractals
• Analogues of the Lebesgue Density Theorem for Fractal Sets of Reals and Integers
• Random fractals
• The Hausdorff dimension of self-affine fractals
• Self‐Similar Random Measures III – Self‐Similar Random Processes
• Fractional Differentiation in the Self-Affine Case III. The Density of the Cantor Set
• Self‐Similar Random Measures. II A Generalization to Self‐Affine Measures
• Sell‐Similar Random Measures. IV – The Recursive Construction Model of Falconer, Graf, and Mauldin and Williams

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