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

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