Electronic Journal of Probability
- Electron. J. Probab.
- Volume 16 (2011), paper no. 13, 362-395.
Central Limit Theorems and Quadratic Variations in Terms of Spectral Density
We give a new proof and provide new bounds for the speed of convergence in the Central Limit Theorem of Breuer Major on stationary Gaussian time series, which generalizes to particular triangular arrays. Our assumptions are given in terms of the spectral density of the time series. We then consider generalized quadratic variations of Gaussian fields with stationary increments under the assumption that their spectral density is asymptotically self-similar and prove Central Limit Theorems in this context.
Electron. J. Probab., Volume 16 (2011), paper no. 13, 362-395.
Accepted: 18 February 2011
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G15: Gaussian processes 60G10: Stationary processes 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62M15: Spectral analysis 62M40: Random fields; image analysis 60H07: Stochastic calculus of variations and the Malliavin calculus
This work is licensed under aCreative Commons Attribution 3.0 License.
Biermé, Hermine; Bonami, Aline; Leon, José R. Central Limit Theorems and Quadratic Variations in Terms of Spectral Density. Electron. J. Probab. 16 (2011), paper no. 13, 362--395. doi:10.1214/EJP.v16-862. https://projecteuclid.org/euclid.ejp/1464820182