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Holderian Weak Invariance Principle for Stationary Mixing Sequences

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  • Davide Giraudo

    (Université de Rouen)

Abstract

We provide some sufficient mixing conditions on a strictly stationary sequence in order to guarantee the weak invariance principle in Hölder spaces. Strong mixing and $$\rho $$ ρ -mixing conditions are investigated as well as $$\tau $$ τ -dependent sequences. The main tools are deviation inequalities for mixing sequences.

Suggested Citation

  • Davide Giraudo, 2017. "Holderian Weak Invariance Principle for Stationary Mixing Sequences," Journal of Theoretical Probability, Springer, vol. 30(1), pages 196-211, March.
    • Handle: RePEc:spr:jotpro:v:30:y:2017:i:1:d:10.1007_s10959-015-0633-9
    DOI: 10.1007/s10959-015-0633-9
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    References listed on IDEAS

    as
    1. J. Dedecker & C. Prieur, 2004. "Coupling for τ-Dependent Sequences and Applications," Journal of Theoretical Probability, Springer, vol. 17(4), pages 861-885, October.
    2. Alfredas Račkauskas & Charles Suquet, 2004. "Necessary and Sufficient Condition for the Functional Central Limit Theorem in Hölder Spaces," Journal of Theoretical Probability, Springer, vol. 17(1), pages 221-243, January.
    3. Dedecker, Jérôme & Doukhan, Paul, 2003. "A new covariance inequality and applications," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 63-80, July.
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