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

Author

Listed:
  • Péter Kevei

    (MTA-SZTE Analysis and Stochastics Research Group, Bolyai Institute
    Center for Mathematical Sciences, Technische Universität München)

  • David M. Mason

    (University of Delaware)

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.

Suggested Citation

  • Péter Kevei & David M. Mason, 2017. "Couplings and Strong Approximations to Time-Dependent Empirical Processes Based on I.I.D. Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 30(3), pages 729-770, September.
    • Handle: RePEc:spr:jotpro:v:30:y:2017:i:3:d:10.1007_s10959-016-0676-6
    DOI: 10.1007/s10959-016-0676-6
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    References listed on IDEAS

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    1. James Kuelbs & Joel Zinn, 2015. "Empirical Quantile Central Limit Theorems for Some Self-Similar Processes," Journal of Theoretical Probability, Springer, vol. 28(1), pages 313-336, March.
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