2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131283We demonstrate the strength of a coupling derived from a Gaussian approximation of Zaitsev (1987a) by revisiting two strong approximation results for the empirical process of Dudley and Philipp (1983), and using the coupling to derive extended and refined versions of them.Published at http://dx.doi.org/10.1214/074921706000000824 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)Statistics TheoryProbability62E17, 62E20 (Primary) 60F15 (Secondary)text