A functional large deviations principle for quadratic forms of Gaussian stationary processes

DOI10.1016/S0167-7152(98)00270-3zbMath0942.60021OpenAlexW2013439783MaRDI QIDQ1292786

Fabrice Gamboa, Alain Rouault, Marguerite Zani

Publication date: 9 August 1999

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-7152(98)00270-3

zbMATH Keywords

Gaussian processesquadratic formslarge deviationsToeplitz matricesWiener-Hopf operators

Mathematics Subject Classification ID

Gaussian processes (60G15) Sums of squares and representations by other particular quadratic forms (11E25) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Large deviations (60F10)

Related Items (10)

Large deviations for quadratic functionals of stable Gauss–Markov chains and entropy production ⋮ Locally adaptive fitting of semiparametric models to nonstationary time series. ⋮ Large deviations for weighted empirical mean with outliers ⋮ Large deviations for drift parameter estimator of mixed fractional Ornstein-Uhlenbeck process ⋮ Estimation of the realized (co-)volatility vector: large deviations approach ⋮ Canonical moments and random spectral measures ⋮ Covariance matrix estimation for stationary time series ⋮ The trace problem for Toeplitz matrices and operators and its impact in probability ⋮ Asymptotic properties of the algebraic moment range process ⋮ Sum rules via large deviations: extension to polynomial potentials and the multi-cut regime

Cites Work

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• On bilinear forms in Gaussian random variables and Toeplitz matrices
• A primer on spectral theory
• Large deviations and variational theorems for marginal problems
• On Toeplitz type quadratic functionals of stationary Gaussian processes
• Bayesian methods and maximum entropy for ill-posed inverse problems
• Large deviations for quadratic functionals of Gaussian processes
• Large deviations for subsampling from individual sequences
• Large deviations for quadratic forms of stationary Gaussian processes
• Integrals which are convex functionals. II

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