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

• Autorzy: Christophe Cuny , Michel Weber
• Języki publikacji: EN

Abstrakty

EN

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 νth moments. We also give an application to the convergence in the mean of the pth moments of certain random trigonometric polynomials built from triangular arrays of independent random variables, thereby extending some recent work of Borwein and Lockhart.

Kategorie tematyczne

• 26D05: Inequalities for trigonometric functions and polynomials
• 28A60: Measures on Boolean rings, measure algebras
• 60G50: Sums of independent random variables; random walks
• 60F05: Central limit and other weak theorems
• 42A05: Trigonometric polynomials, inequalities, extremal problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 106
• Numer: 1
• Strony: 147-160

Daty

wydano

2006

Twórcy

autor

Christophe Cuny

• Équipe ERIM, Université de la Nouvelle-Calédonie, B.P. 4477, F-98847 Noumea Cedex, Nouvelle-Calédonie

autor

Michel Weber

• UFR de Mathématique (IRMA), Université Louis-Pasteur et CNRS, 7 rue René Descartes, F-67084 Strasbourg Cedex, France

Identyfikatory

DOI

10.4064/cm106-1-13