Representation of Euclidean Random Field

DOI10.1017/S0027763000000714zbMath0594.60054MaRDI QIDQ3725268

Shigeo Takenaka

Publication date: 1987

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

fractional Brownian motioninvariant measureEuclidean random fieldtheory of fractals

Mathematics Subject Classification ID

Random fields (60G60) Geometric probability and stochastic geometry (60D05) Integral geometry (53C65)

Related Items (6)

An integrated fractional Fourier transform ⋮ Generalized Radon Transform and Lévy’s Brownian Motion, II ⋮ Integral-geometric construction of self-similar stable processes ⋮ Invariance principles for self-similar set-indexed random fields ⋮ Anisotropic fractional Brownian random fields as white noise functionals ⋮ Nonexistence of fractional Brownian fields indexed by cylinders

Cites Work

• Lévy's Brownian motion as a set-indexed process and a related central limit theorem
• A statistically important Gaussian process
• Generalized Radon Transform and Lévy’s Brownian Motion, II
• A unified radon inversion formula
• Independence of the increments of Gaussian random fields
• On Representation of Lévy’s Fields by Indicators
• Brownian motion parametrized with metric space of constant curvature

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