On the convergence of moments in the CLT for triangular arrays with an application to random polynomials
Volume 106 / 2006
Colloquium Mathematicum 106 (2006), 147-160
MSC: Primary 60F05, 60G50, 42A05; Secondary 26D05, 28A60.
DOI: 10.4064/cm106-1-13
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 $\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.
