Weakly stationary stochastic processes valued in a separable Hilbert space: Gramian-cramér representations and applications

DOI10.1051/ps/2023014arXiv1910.08491OpenAlexW3199376551MaRDI QIDQ6197997

Amaury Durand, François Roueff

Publication date: 20 February 2024

Published in: ESAIM: Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.08491

zbMATH Keywords

functional time seriesisometries on Hilbert modulesspectral representation of random processes

Mathematics Subject Classification ID

General second-order stochastic processes (60G12) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Vector-valued measures and integration (46G10)

Cites Work

• Fourier analysis of stationary time series in function space
• Operator self-similar processes and functional central limit theorems
• Locally stationary functional time series
• Limit theorems for Hilbert space-valued linear processes under long range dependence
• A note on Herglotz's theorem for time series on function spaces
• The central limit theorem for a sequence of random processes with space-varying long memory
• Cramér-Karhunen-Loève representation and harmonic principal component analysis of functional time series
• Naimark's moment theorem
• OPERATOR FRACTIONAL BROWNIAN MOTION AS LIMIT OF POLYGONAL LINES PROCESSES IN HILBERT SPACE
• Mathematical Foundations of Signal Processing
• Long-Range Dependent Curve Time Series
• Long-Range Dependence and Self-Similarity
• Dynamic Functional Principal Components
• ON THE VITALI-HAHN-SAKS AND NIKODÝM THEOREMS
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