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Exact L 2 Small Balls of Gaussian Processes

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Abstract

We prove a comparison theorem extending Li(6) and develop a complex-analytic approach to treat L 2 small ball probabilities of Gaussian processes. We demonstrate the techniques for the m-times integrated Brownian motions and in examples where one can not apply Li comparison theorem.

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Authors and Affiliations

  1. Department of Mathematics, University of Idaho, Moscow, Idaho, 83844-1103

    F. Gao

  2. Department of Statistics, Colorado State University, Ft. Collins, Colorado, 80523-1877

    J. Hannig

  3. Mathematics Department, University of Maryland, College Park, Maryland, 20742-4015

    T.-Y. Lee

  4. Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, Maryland, 21218-2682

    F. Torcaso

Authors
  1. F. Gao
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  2. J. Hannig
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  3. T.-Y. Lee
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  4. F. Torcaso
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Correspondence to F. Torcaso.

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Gao, F., Hannig, J., Lee, TY. et al. Exact L 2 Small Balls of Gaussian Processes. Journal of Theoretical Probability 17, 503–520 (2004). https://doi.org/10.1023/B:JOTP.0000020705.28185.4c

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  • DOI: https://doi.org/10.1023/B:JOTP.0000020705.28185.4c

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