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arXiv · 1308.4939

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

Péter Kevei·David M. Mason
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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.

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Péter Kevei, David M. Mason. 2016-06-20. Couplings and Strong Approximations to Time Dependent Empirical Processes Based on I.I.D. Fractional Brownian Motions. https://doi.org/10.1007/s10959-016-0676-6

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