Metric entropy of integration operators and small ball probabilites for the Brownian sheet

DOI10.1006/jath.1999.3354zbMath0945.47022OpenAlexW2053302979MaRDI QIDQ1960901

Werner Linde, Thomas Kühn, Thomas Dunker, Mikhail Lifshits

Publication date: 4 October 2000

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

Full work available at URL: https://doi.org/10.1006/jath.1999.3354

zbMATH Keywords

Brownian sheetmetric entropysmall ball probabilities\(d\)-dimensional integration operatorKolmogorov and entropy numbers

Mathematics Subject Classification ID

Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06) Linear operators on function spaces (general) (47B38)

Related Items (7)

Small deviations of stable processes and entropy of the associated random operators ⋮ Estimates for the entropy numbers of the Nikol'skii–Besov classes of functions with mixed smoothness in the space of quasi‐continuous functions ⋮ The Lasso with structured design and entropy of (absolute) convex hulls ⋮ Metric entropy of high dimensional distributions ⋮ Gaussian approximation numbers and metric entropy ⋮ Small ball probabilities for the Slepian Gaussian fields ⋮ Relations between classical, average, and probabilistic Kolmogorov widths

Cites Work

• Probability estimates for multiparameter Brownian processes
• s-numbers of integral operators with Hölder continuous kernels over metric compacta
• Entropy numbers, s-numbers, and eigenvalue problems
• Comparison results for the lower tail of Gaussian seminorms
• Estimates of entropy numbers and Gaussian measures for classes of functions with bounded mixed derivative
• Metric entropy and the small ball problem for Gaussian measures
• The small ball problem for the Brownian sheet
• Small ball problem via wavelets for Gaussian processes
• Approximation, metric entropy and small ball estimates for Gaussian measures
• Estimates for the small ball probabilities of the fractional Brownian sheet
• An inequality for trigonometric polynomials and its application for estimating the entropy numbers
• Small ball probabilities of Gaussian fields
• Some small ball probabilities for Gaussian processes under nonuniform norms
• On probabilities of small deviations for stochastic processes
• Subspaces of Small Codimension of Finite-Dimensional Banach Spaces
• Entropy Numbers and Approximation Numbers in Function Spacess
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