Couplings and Strong Approximations to Time Dependent Empirical Processes Based on I.I.D. Fractional Brownian Motions

Abstract

We define a time dependent empirical process based on $n$ i.i.d.~fractional Brownian motions and establish Gaussian couplings and strong approximations to it by Gaussian processes. They lead to functional laws of the iterated logarithm for this process.

To appear in the Journal of Theoretical Probability. 37 pages. Corrected version. The results on quantile processes are taken out and it will appear elsewhere

References in corpus (3)

• Revisiting two strong approximation results of Dudley and Philipp
• Weak Convergence of the Scaled Median of Independent Brownian Motions
• A CLT for empirical processes involving time-dependent data