Central Limit Theorems and Quadratic Variation in terms of Spectral Density - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2010

Central Limit Theorems and Quadratic Variation in terms of Spectral Density

Hermine Biermé
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José R. Leon
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Résumé

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.
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Dates et versions

hal-00497795 , version 1 (05-07-2010)
hal-00497795 , version 2 (01-08-2010)

Identifiants

  • HAL Id : hal-00497795 , version 1

Citer

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