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Computing the Distribution of the Maximum of Gaussian Random Processes

Author

Listed:
  • Christine Cierco-Ayrolles

    (Université Paul Sabatier, INRA)

  • Alain Croquette

    (Université Paul Sabatier)

  • Céline Delmas

    (INRA)

Abstract

The aim of this paper is to propose an Splus program to calculate bounds for the distribution of the maximum of a smooth Gaussian process on a fixed interval. We generalize the results given in Azaïs et al. (1999) to the case of the absolute value of the Gaussian process and to the non-homogeneous case. Our method relies on calculations of the first three terms of the Rice's series. Some applications are given to illustrate the method and the performances of the program. The corresponding Splus functions are available at the URL: http://www.lsp.ups-tlse.fr/Cdelmas/software.html.

Suggested Citation

  • Christine Cierco-Ayrolles & Alain Croquette & Céline Delmas, 2003. "Computing the Distribution of the Maximum of Gaussian Random Processes," Methodology and Computing in Applied Probability, Springer, vol. 5(4), pages 427-438, December.
    • Handle: RePEc:spr:metcap:v:5:y:2003:i:4:d:10.1023_a:1026233412905
    DOI: 10.1023/A:1026233412905
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    Cited by:

    1. Andrew M. Ross, 2010. "Computing Bounds on the Expected Maximum of Correlated Normal Variables," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 111-138, March.
    2. Shuzhuan Zheng & Lijian Yang & Wolfgang Karl Härdle, 2011. "A Confidence Corridor for Sparse Longitudinal Data Curves," SFB 649 Discussion Papers SFB649DP2011-002, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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