Central Limit Theorems and Quadratic Variation in terms of Spectral Density

Hermine Biermé (1) , Aline Bonami (2) , José R. Leon (3)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
3 UCV - Universidad Central de Venezuela

We give a new proof and provide new bounds for the speed of convergence in the Central Limit Theorems of Breuer Major on stationary Gaussian time series. 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.

Mots clés: Central limit theorem; Gaussian stationary process; Spectral density; Periodogram; Quadratic variations

Domaines: Probabilités [math.PR]

Hermine Biermé, Aline Bonami, José R. Leon. Central Limit Theorems and Quadratic Variation in terms of Spectral Density. 2010. ⟨hal-00497795v1⟩