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

Volume 106 / 2006

Christophe Cuny, Michel Weber Colloquium Mathematicum 106 (2006), 147-160 MSC: Primary 60F05, 60G50, 42A05; Secondary 26D05, 28A60. DOI: 10.4064/cm106-1-13


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.


  • Christophe CunyÉquipe ERIM
    Université de la Nouvelle-Calédonie
    B.P. 4477
    F-98847 Noumea Cedex, Nouvelle-Calédonie
  • Michel WeberUFR de Mathématique (IRMA)
    Université Louis-Pasteur et CNRS
    7 rue René Descartes
    F-67084 Strasbourg Cedex, France

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