Rates of clustering for some Gaussian self-similar processes

DOI10.1007/BF01193582zbMath0695.60040OpenAlexW2094622812MaRDI QIDQ910093

James Kuelbs, Victor W. Goodman

Publication date: 1991

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01193582

zbMATH Keywords

Brownian motionGaussian processesBrownian sheetfunctional law of the iterated logarithmself-similar Gaussian processes

Mathematics Subject Classification ID

Gaussian processes (60G15) Brownian motion (60J65) Functional limit theorems; invariance principles (60F17)

Related Items (19)

Lévy area of Wiener processes in Banach spaces ⋮ Strassen-type functional laws for strong topologies ⋮ Small values of Gaussian processes and functional laws of the iterated logarithm ⋮ Rates of clustering in FLIL for weighted partial sum processes ⋮ Functional limit theorems for \(d\)-dimensional FBM in Hölder norm ⋮ Limits for partial maxima of Gaussian random vectors ⋮ A CLT for empirical processes involving time-dependent data ⋮ Exact rate of convergence in Strassen's law of the iterated logarithm ⋮ Functional limit theorems for C-R increments of \(k\)-dimensional Brownian motion in Hölder norm ⋮ Exact convergence rates for the bounded law of the iterated logarithm in Hilbert space ⋮ The fractal nature of the functional law of logarithm of fractional Brownian motions ⋮ Functional limit theorems for the increments of Gaussian samples ⋮ Functional limit theorems for the increments of \(d\)-dimensional Gaussian processes in a Hölder type norm ⋮ Functional limit theorems for the infinite series of OU processes in Hölder norm ⋮ A lim inf result in Strassen's law of the iterated logarithm ⋮ On the large increments of fractional Brownian motion ⋮ Exact rates of convergence of functional limit theorems for Csörgő-Révész increments of a Wiener process. ⋮ New Gaussian estimates for enlarged balls ⋮ Functional limit theorems for \(C\)-\(R\) increments of \(l^p\)-valued Wiener processes in the Hölder norm

Cites Work

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• Rates of clustering in Strassen's LIL for Brownian motion
• On the rate of convergence in Strassen's law of the iterated logarithm
• Probability estimates for multiparameter Brownian processes
• Rates of convergence for increments of Brownian motion
• Some results on the LIL in Banach space with applications to weighted empirical processes
• A strong convergence theorem for Banach space valued random variables
• On the speed of convergence in Strassen's law of the iterated logarithm
• Sur l’intégrabilité des vecteurs gaussiens
• A Multi-Parameter Gaussian Process
• Fractional Brownian Motions, Fractional Noises and Applications

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