Kolmogorov numbers of Riemann-Liouville operators over small sets and applications to Gaussian processes

DOI10.1016/j.jat.2004.04.011zbMath1066.47017OpenAlexW1975074544MaRDI QIDQ596813

Werner Linde

Publication date: 10 August 2004

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2004.04.011

zbMATH Keywords

fractional Brownian motionfractional integrationfractal setsentropy numberssmall deviationKolmogorov numbersdegree of compactness

Mathematics Subject Classification ID

Gaussian processes (60G15) Fractional derivatives and integrals (26A33) Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06) Fractals (28A80)

Related Items

Compactness properties of certain integral operators related to fractional integration, Nondeterminism of linear operators and lower entropy estimates, Entropy numbers of convex hulls in Banach spaces and applications, Small deviation probability via chaining

Cites Work

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• A note on small ball probability of a Gaussian process with stationary increments
• s-numbers of integral operators with Hölder continuous kernels over metric compacta
• Entropy numbers of diagonal operators between symmetric Banach spaces
• Metric entropy and the small ball problem for Gaussian measures
• Small values of Gaussian processes and functional laws of the iterated logarithm
• Entropy of \(C(X)\)-valued operators and diverse applications
• Approximation, metric entropy and small ball estimates for Gaussian measures
• Relations between classical, average, and probabilistic Kolmogorov widths
• Optimal series representation of fractional Brownian sheets
• Small ball probabilities of fractional Brownian sheets via fractional integration operators
• Entropy of \(C(K)\)-valued operators
• Small deviations for fractional stable processes
• Evaluating the small deviation probabilities for subordinated Lévy processes
• The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
• Subspaces of Small Codimension of Finite-Dimensional Banach Spaces
• DIAMETERS OF SOME FINITE-DIMENSIONAL SETS AND CLASSES OF SMOOTH FUNCTIONS
• Existence of small ball constants for fractional Brownian motions
• Metric Entropy of Convex Hulls in Banach Spaces
• Fractional Brownian Motions, Fractional Noises and Applications