An optimal series expansion of the multiparameter fractional Brownian motion

DOI10.1007/s10959-007-0122-xzbMath1139.60318arXivmath/0411539OpenAlexW2096623618MaRDI QIDQ927255

Anatoliy Malyarenko

Publication date: 4 June 2008

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0411539

zbMATH Keywords

Fractional Brownian motionRate optimal expansionSeries expansion

Mathematics Subject Classification ID

Gaussian processes (60G15)

Related Items (3)

A Family of Series Representations of the Multiparameter Fractional Brownian Motion ⋮ On Haar expansion of Riemann-Liouville process in a critical case ⋮ Series representations and simulations of isotropic random fields in the Euclidean space

Cites Work

• A series expansion of fractional Brownian motion
• A rate-optimal trigonometric series expansion of the fractional Brownian motion
• Functional limit theorems for multiparameter fractional Brownian motion
• Representations of isotropic Gaussian random fields with homogeneous increments
• Approximation, metric entropy and small ball estimates for Gaussian measures
• Optimal series representation of fractional Brownian sheets
• Weak convergence and empirical processes. With applications to statistics
• Approximation of Gaussian random fields: General results and optimal wavelet representation of the Lévy fractional motion
• Optimality of an explicit series expansion of the fractional Brownian sheet
• Fractional Brownian Motions, Fractional Noises and Applications
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