Gebelein inequality in a Hilbert space

DOI10.4064/AM2478-1-2024zbMATH Open1543.60005MaRDI QIDQ6569315

Marek Beśka

Publication date: 9 July 2024

Published in: Applicationes Mathematicae (Search for Journal in Brave)

zbMATH Keywords

Hermite polynomialsOrnstein-Uhlenbeck operatorGaussian random vectorCameron-Martin spacewhite noise mapping

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Measures and integration on abstract linear spaces (46G12) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Probability theory on linear topological spaces (60B11) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Cites Work

• Correlation inequalities and applications to vector-valued Gaussian random variables and fractional Brownian motion
• Das statistische Problem der Korrelation als Variations und Eigenwertproblem und sein Zusammenhang mit der Ausgleichsrechnung.
• The Malliavin Calculus and Related Topics
• Note on the variance of the sum of Gaussian functionals
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