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

Péter Kevei () and David M. Mason ()
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Péter Kevei: MTA-SZTE Analysis and Stochastics Research Group, Bolyai Institute
David M. Mason: University of Delaware

Journal of Theoretical Probability, 2017, vol. 30, issue 3, 729-770

Abstract: 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.

Keywords: Coupling inequality; Fractional Brownian motion; Strong approximation; Time-dependent empirical process; 62E17; 60G22; 60F15 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10959-016-0676-6

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