Geodesic
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 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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

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 
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     title = {On the convergence of moments in the {CLT} for
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     journal = {Colloquium Mathematicum},
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 triangular arrays with an application
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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

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