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On the regularity of the distribution of the maximum of one-parameter Gaussian processes
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  • Published: January 2001

On the regularity of the distribution of the maximum of one-parameter Gaussian processes

  • Jean-Marc Azaïs1 &
  • Mario Wschebor1 

Probability Theory and Related Fields volume 119, pages 70–98 (2001)Cite this article

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  • 9 Citations

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Abstract.

The main result in this paper states that if a one-parameter Gaussian process has C 2k paths and satisfies a non-degeneracy condition, then the distribution of its maximum on a compact interval is of class C k. The methods leading to this theorem permit also to give bounds on the successive derivatives of the distribution of the maximum and to study their asymptotic behaviour as the level tends to infinity.

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Authors and Affiliations

  1. Laboratoire de Statistique et Probabilités, UMR-CNRS C55830, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 4. France. e-mail: azais@cict.fr, , , , , , FR

    Jean-Marc Azaïs & Mario Wschebor

Authors
  1. Jean-Marc Azaïs
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  2. Mario Wschebor
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Received: 14 May 1999 / Revised version: 18 October 1999 / Published online: 14 December 2000

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Azaïs, JM., Wschebor, M. On the regularity of the distribution of the maximum of one-parameter Gaussian processes. Probab Theory Relat Fields 119, 70–98 (2001). https://doi.org/10.1007/PL00012739

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  • Issue Date: January 2001

  • DOI: https://doi.org/10.1007/PL00012739

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  • Mathematics Subject Classification (2000): 60G15, 60Gxx, 60E05
  • Key words or phrases: Extreme values – Distribution of the maximum
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