BY MEANS OF LINDEBERG’S CENTRAL LIMIT THEOREM

Abstract

We study the construction of a version of standard Brownian sheet called h -generalized standard
Brownian sheet. It is shown by means of Lindeberg’s theorem that it is a limit process of a sequence of
partial sums processes of independent random variables in the sense of weak convergence in the metric
space of continuous functions on the compact region [0,1]×[0,1]. Based on this convergence we
approximate by simulation the quantiles of Kolmogorov, Kolmogorov-Smirnov and Cramér-von Mises
type statistics which are defined as continuous functionals of the process.