Necessary conditions for nonlinear functionals of Gaussian processes to satisfy central limit theorems
From MaRDI portal
Publication:1263157
DOI10.1016/0304-4149(89)90055-0zbMath0687.60024OpenAlexW2058169839MaRDI QIDQ1263157
Eric V. Slud, Daniel W. Chambers
Publication date: 1989
Published in: Stochastic Processes and their Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0304-4149(89)90055-0
Gaussian processmultiple Wiener-Itô integralsstochastic integral representationWiener-Itô expansionrepresentation of functionalstime-shift operators
Gaussian processes (60G15) Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10) Martingales with continuous parameter (60G44) Functional limit theorems; invariance principles (60F17)
Related Items
Variance of the number of zeroes of shift-invariant Gaussian analytic functions, Noncentral convergence of multiple integrals, Asymptotics for the local time of a strongly dependent vector-valued Gaussian random field, Averaging Gaussian functionals, Continuous Breuer-Major theorem: tightness and nonstationarity, On tightness and weak convergence in the approximation of the occupation measure of fractional Brownian motion, Gaussian scenario for the heat equation with quadratic potential and weakly dependent data with applications, Quantitative central limit theorems of spherical sojourn times of isotropic Gaussian fields, Multiple Wiener-Itô integral expansions for level-crossing-count functionals, Limit theorems for weighted nonlinear transformations of Gaussian stationary processes with singular spectra, How the instability of ranks under long memory affects large-sample inference, Reduction principle for functionals of strong-weak dependent vector random fields, Integrated functionals of normal and fractional processes, Berry-Esseen bounds in the Breuer-major CLT and Gebelein's inequality, A mixture-type limit theorem for nonlinear functions of Gaussian sequences
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Central limit theorems for non-linear functionals of Gaussian fields
- Noncentral limit theorems for quadratic forms in random variables having long-range dependence
- Wiener functionals and probability limit theorems. I: The central limit theorems
- Remarks on limit theorems for nonlinear functionals of Gaussian sequences
- Wiener functionals and probability limit theorems. II: Term-wise multiplication and its applications
- Multiple Wiener-Ito integrals. With applications to limit theorems
- A central limit theorem for the number of zeros of a stationary Gaussian process
- Gaussian and their subordinates self-similar random generalized fields
- Dependent central limit theorems and invariance principles
- CLT and other limit theorems for functionals of Gaussian processes
- Weak convergence to fractional brownian motion and to the rosenblatt process
- On the functional central limit theorem for martingales
- Some limit theorems for partial sums of quadratic forms in stationary Gaussian variables
- Non-central limit theorems for non-linear functional of Gaussian fields
- Remarks on the functional central limit theorem for martingales
- Martingale Integrals
