Chapter 8. The Tail of the Distribution of the Maximum

  1. Jean-Marc Azäis1 and
  2. Mario Wschebor2

Published Online: 21 JUL 2008

DOI: 10.1002/9780470434642.ch8

Level Sets and Extrema of Random Processes and Fields

Level Sets and Extrema of Random Processes and Fields

How to Cite

Azäis, J.-M. and Wschebor, M. (2009) The Tail of the Distribution of the Maximum, in Level Sets and Extrema of Random Processes and Fields, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470434642.ch8

Author Information

  1. 1

    Université de Toulouse, Institut de Mathématiques, Laboratoire de Statistiques et Probabilités, Toulouse, France

  2. 2

    Universidad de la República, Centro de Matemática, Facultad de Ciencias, Montevideo, Uruguay

Publication History

  1. Published Online: 21 JUL 2008
  2. Published Print: 27 FEB 2009

ISBN Information

Print ISBN: 9780470409336

Online ISBN: 9780470434642

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Keywords:

  • tail of distribution of maximum;
  • one-dimensional parameter - asymptotic behavior of derivatives of FM;
  • an application to unbounded processes

Summary

This chapter contains sections titled:

  • One-Dimensional Parameter: Asymptotic Behavior of the Derivatives of FM

  • An Application to Unbounded Processes

  • A General Bound for pM

  • Computing p̄(x) for Stationary Isotropic Gaussian Fields

  • Asymptotics as x [RIGHTWARDS ARROW] + ∞

  • Examples

  • Exercises