Strong approximation for set-indexed partial sum processes via kmt constructions III

Abstract

We generalize the results of Komlos, Major and Tusnady concerning the strong approximation of partial sums of independent and identically distributed random variables with a finite μ-th moment to the case when the parameter set is two-dimensional. The most striking result is that the rates of convergence are exactly the same as in the one-dimensional case. © 1997 Société de Mathématiques Appliquées et Industrielles. Typeset by AMS-TEX.