Extending results by P. 1981--1983 we give strong approximation results for sample maxima by simple transformations of extremal processes and discuss the quality of the approximations. The limiting process becomes stationary after a transformation of the argument.
"Stong approximation of maxima by extremal processes." Ann. Probab. 31 (2) 926 - 947, April 2003. https://doi.org/10.1214/aop/1048516541