We obtain a strong approximation for the empirical process of n observe delements of a GARCH sequence. The weak convergence of the empirical process and the law of the iterated logarithm are immediate consequences.
"Strong approximation of the empirical process of Garch sequences." Ann. Appl. Probab. 11 (3) 789 - 809, August 2001. https://doi.org/10.1214/aoap/1015345349