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

Christophe Cuny, and Michel Weber. "On the convergence of moments in the CLT for triangular arrays with an application to random polynomials." Colloquium Mathematicae 106.1 (2006): 147-160. <http://eudml.org/doc/283579>.

@article{ChristopheCuny2006,
abstract = {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.},
author = {Christophe Cuny, Michel Weber},
journal = {Colloquium Mathematicae},
keywords = {central limit theorem; independent random variables; Lindeberg-Lyapunov condition; weighted sums; -norm; random trigonometric polynomial},
language = {eng},
number = {1},
pages = {147-160},
title = {On the convergence of moments in the CLT for triangular arrays with an application to random polynomials},
url = {http://eudml.org/doc/283579},
volume = {106},
year = {2006},
}

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 Mathematicae
PY - 2006
VL - 106
IS - 1
SP - 147
EP - 160
AB - 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.
LA - eng
KW - central limit theorem; independent random variables; Lindeberg-Lyapunov condition; weighted sums; -norm; random trigonometric polynomial
UR - http://eudml.org/doc/283579
ER -