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Small Ball Estimates for Gaussian Processes under Sobolev Type Norms

Author

Listed:
  • Wenbo V. Li

    (University of Delaware)

  • Qi-Man Shao

    (University of Oregon)

Abstract

A sharp small ball estimate under Sobolev type norms is obtained for certain Gaussian processes in general and for fractional Brownian motions in particular. New method using the techniques in large deviation theory is developed for small ball estimates. As an application the Chung's LIL for fractional Brownian motions is given in this setting.

Suggested Citation

  • Wenbo V. Li & Qi-Man Shao, 1999. "Small Ball Estimates for Gaussian Processes under Sobolev Type Norms," Journal of Theoretical Probability, Springer, vol. 12(3), pages 699-720, July.
    • Handle: RePEc:spr:jotpro:v:12:y:1999:i:3:d:10.1023_a:1021675731663
    DOI: 10.1023/A:1021675731663
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    References listed on IDEAS

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    1. Csörgo, Miklós & Horváth, Lajos & Shao, Qi-Man, 1993. "Convergence of integrals of uniform empirical and quantile processes," Stochastic Processes and their Applications, Elsevier, vol. 45(2), pages 283-294, April.
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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. Siegfried Graf & Harald Luschgy & Gilles Pagès, 2003. "Functional Quantization and Small Ball Probabilities for Gaussian Processes," Journal of Theoretical Probability, Springer, vol. 16(4), pages 1047-1062, October.

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