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Estimates for the Small Ball Probabilities of the Fractional Brownian Sheet

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  • Thomas Dunker

    (Friedrich Schiller Universität)

Abstract

We obtain some new estimates for the small ball behavior of the d-dimensional fractional Brownian sheet under Hölder and Orlicz norms. For d=2, these bounds are sharp for the Orlicz and the sup-norm. In addition, we give bounds for the Kolmogorov and entropy numbers of some operators satisfying an L 2-Hölder-type condition.

Suggested Citation

  • Thomas Dunker, 2000. "Estimates for the Small Ball Probabilities of the Fractional Brownian Sheet," Journal of Theoretical Probability, Springer, vol. 13(2), pages 357-382, April.
    • Handle: RePEc:spr:jotpro:v:13:y:2000:i:2:d:10.1023_a:1007897525164
    DOI: 10.1023/A:1007897525164
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    Cited by:

    1. S. Dereich & F. Fehringer & A. Matoussi & M. Scheutzow, 2003. "On the Link Between Small Ball Probabilities and the Quantization Problem for Gaussian Measures on Banach Spaces," Journal of Theoretical Probability, Springer, vol. 16(1), pages 249-265, January.
    2. David M. Mason & Zhan Shi, 2001. "Small Deviations for Some Multi-Parameter Gaussian Processes," Journal of Theoretical Probability, Springer, vol. 14(1), pages 213-239, January.
    3. Eduard Belinsky & Werner Linde, 2002. "Small Ball Probabilities of Fractional Brownian Sheets via Fractional Integration Operators," Journal of Theoretical Probability, Springer, vol. 15(3), pages 589-612, July.

    More about this item

    Keywords

    Gaussian field; small ball probabilities;

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