Asymptotic analysis via Mellin transforms for small deviations in \(L^2\)-norm of integrated Brownian sheets

DOI10.1007/s00440-004-0363-xzbMath1052.60027arXivmath/0309391OpenAlexW2113364692MaRDI QIDQ1884727

James Allen Fill, Fred Torcaso

Publication date: 5 November 2004

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

Full work available at URL: https://arxiv.org/abs/math/0309391

zbMATH Keywords

Mellin transformasymptoticssmall deviationsreversionharmonic sumgeneralized Dirichlet seriesintegrated Brownian sheet

Mathematics Subject Classification ID

Gaussian processes (60G15) Characteristic functions; other transforms (60E10) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Inverse theorems in approximation theory (41A27)

Related Items (14)

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Cites Work

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• Laplace transforms via {H}adamard factorization
• On the Lambert \(w\) function
• Exact \(L^2\) small balls of Gaussian processes
• Exact \(L_2\)-small ball behavior of integrated Gaussian processes and spectral asymptotics of boundary value problems
• Chung’s law for integrated Brownian motion
• A Generalized Logarithm for Exponential-Linear Equations

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