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Journal of Theoretical Probability

, Volume 30, Issue 3, pp 729–770 | Cite as

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

  • Péter KeveiEmail author
  • David M. Mason
Article

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 

Mathematics Subject Classification (2010)

62E17 60G22 60F15 

Notes

Acknowledgments

The authors thank the Associate Editor for a comment that led to Remark 1. PK was partially supported by the Hungarian Scientific Research Fund OTKA PD106181, by the European Union and co-funded by the European Social Fund under the project ‘Telemedicine-focused research activities on the field of Mathematics, Informatics and Medical sciences’ of project number TÁMOP-4.2.2.A-11/1/KONV-2012-0073, and by a postdoctoral fellowship of the Alexander von Humboldt Foundation.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.MTA-SZTE Analysis and Stochastics Research Group, Bolyai InstituteSzegedHungary
  2. 2.Center for Mathematical Sciences, Technische Universität MünchenGarchingGermany
  3. 3.Department of Applied Economics and StatisticsUniversity of DelawareNewarkUSA

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