The limit process of the difference between the empirical distribution function and its concave majorant

We consider the process F^n-Fn, being the difference between the empirical distribution function Fn and its least concave majorant F^n, corresponding to a sample from a decreasing density. We extend Wang's result on pointwise convergence of F^n-Fn and prove that this difference converges as a process in distribution to the corresponding process for two-sided Brownian motion with parabolic drift.