Fractal Dimensions for Some Increments of the Uniform Empirical Process

In this paper, we investigate the limiting behavior of increments of the uniform empirical process. More precisely, we are concerned by sets of exceptional oscillation points related to large and small increments. We prove that these sets are random fractals and evaluate their Hausdorff dimensions. This work is a complement to the previous investigations carried out by Deheuvels and Mason(6) where Csörgő–Révész–Stute-type increments are studied.