On the convergence of moments in the CLT for
 triangular arrays with an application
 to random polynomials

Christophe Cuny; Michel Weber

doi:10.4064/cm106-1-13

Geodesic

Parcourir par

On the convergence of moments in the CLT for triangular arrays with an application to random polynomials

Christophe Cuny ¹ ; Michel Weber ²

¹ Équipe ERIM Université de la Nouvelle-Calédonie B.P. 4477 F-98847 Noumea Cedex, Nouvelle-Calédonie
² UFR de Mathématique (IRMA) Université Louis-Pasteur et CNRS 7 rue René Descartes F-67084 Strasbourg Cedex, France

Colloquium Mathematicum, Tome 106 (2006) no. 1, pp. 147-160.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

We give a proof of convergence of moments in the Central Limit Theorem (under the Lyapunov–Lindeberg condition) for triangular arrays, yielding a new estimate of the speed of convergence expressed in terms of $\nu $th moments. We also give an application to the convergence in the mean of the $p$th moments of certain random trigonometric polynomials built from triangular arrays of independent random variables, thereby extending some recent work of Borwein and Lockhart.

DOI : 10.4064/cm106-1-13

Keywords: proof convergence moments central limit theorem under lyapunov lindeberg condition triangular arrays yielding estimate speed convergence expressed terms moments application convergence mean pth moments certain random trigonometric polynomials built triangular arrays independent random variables thereby extending recent work borwein lockhart

Affiliations des auteurs :

Christophe Cuny ¹ ; Michel Weber ²

@article{10_4064_cm106_1_13,
     author = {Christophe Cuny and Michel Weber},
     title = {On the convergence of moments in the {CLT} for
 triangular arrays with an application
 to random polynomials},
     journal = {Colloquium Mathematicum},
     pages = {147--160},
     publisher = {mathdoc},
     volume = {106},
     number = {1},
     year = {2006},
     doi = {10.4064/cm106-1-13},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm106-1-13/}
}

TY  - JOUR
AU  - Christophe Cuny
AU  - Michel Weber
TI  - On the convergence of moments in the CLT for
 triangular arrays with an application
 to random polynomials
JO  - Colloquium Mathematicum
PY  - 2006
SP  - 147
EP  - 160
VL  - 106
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm106-1-13/
DO  - 10.4064/cm106-1-13
LA  - en
ID  - 10_4064_cm106_1_13
ER  -

%0 Journal Article
%A Christophe Cuny
%A Michel Weber
%T On the convergence of moments in the CLT for
 triangular arrays with an application
 to random polynomials
%J Colloquium Mathematicum
%D 2006
%P 147-160
%V 106
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm106-1-13/
%R 10.4064/cm106-1-13
%G en
%F 10_4064_cm106_1_13

Christophe Cuny; Michel Weber. On the convergence of moments in the CLT for
 triangular arrays with an application
 to random polynomials. Colloquium Mathematicum, Tome 106 (2006) no. 1, pp. 147-160. doi : 10.4064/cm106-1-13. http://geodesic.mathdoc.fr/articles/10.4064/cm106-1-13/

Cité par Sources :