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Central Limit Theorems and Quadratic Variations in Terms of Spectral Density


 
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1. Title Title of document Central Limit Theorems and Quadratic Variations in Terms of Spectral Density
 
2. Creator Author's name, affiliation, country Hermine Biermé; Université Paris-Descartes - Paris 5; France
 
2. Creator Author's name, affiliation, country Aline Bonami; Université d'Orléans; France
 
2. Creator Author's name, affiliation, country José R. Leon; Universidad Central de Venezuela; Venezuela
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Central limit theorem; Gaussian stationary process; spectral density; periodogram; quadratic variations; fractional Brownian Motion
 
3. Subject Subject classification 60F05; 60G15; 60G10; 62M10; 62M15; 62M40; 60H07
 
4. Description Abstract 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ANR-09-BLAN-0029-01 and ANR-07- BLAN-0247-01
 
7. Date (YYYY-MM-DD) 2011-02-18
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/862
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-862
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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