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Strong Invariance Principles with Rate for “Reverse” Martingale Differences and Applications

Author

Listed:
  • Christophe Cuny

    (Grande Voie des Vignes)

  • Florence Merlevède

    (Université Paris Est, LAMA, CNRS UMR 8050)

Abstract

In this paper, we obtain almost sure invariance principles with rate of order $$n^{1/p}\log ^\beta n$$ n 1 / p log β n , $$2

Suggested Citation

  • Christophe Cuny & Florence Merlevède, 2015. "Strong Invariance Principles with Rate for “Reverse” Martingale Differences and Applications," Journal of Theoretical Probability, Springer, vol. 28(1), pages 137-183, March.
  • Handle: RePEc:spr:jotpro:v:28:y:2015:i:1:d:10.1007_s10959-013-0506-z
    DOI: 10.1007/s10959-013-0506-z
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    References listed on IDEAS

    as
    1. Shao, Qi-Man, 1993. "Almost sure invariance principles for mixing sequences of random variables," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 319-334, November.
    2. Dedecker, Jérôme & Prieur, Clémentine, 2007. "An empirical central limit theorem for dependent sequences," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 121-142, January.
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