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The functional law of the iterated logarithm for von Mises functionals and multiple Wiener integrals

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  • Dehling, Herold

Abstract

We prove a functional law of the iterated logarithm (FLIL) for m-variate von-Mies-functionals and U-statistics, thereby extending the bounded LIL, recently established by Dehling, Denker and Philipp. Using an almost sure invariance principle for von-Mises-functionals this result also implies the FLIL for multiple Wiener integrals.

Suggested Citation

  • Dehling, Herold, 1989. "The functional law of the iterated logarithm for von Mises functionals and multiple Wiener integrals," Journal of Multivariate Analysis, Elsevier, vol. 28(2), pages 177-189, February.
    • Handle: RePEc:eee:jmvana:v:28:y:1989:i:2:p:177-189
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    Cited by:

    1. Koltchinskii, Vladimir & Nickl, Richard & van de Geer, Sara & Wellner, Jon A., 2016. "The mathematical work of Evarist Giné," Stochastic Processes and their Applications, Elsevier, vol. 126(12), pages 3607-3622.
    2. Arcones, Miguel A. & Giné, Evarist, 1995. "On the law of the iterated logarithm for canonical U-statistics and processes," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 217-245, August.

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