Higher Order Approximations For Maxima Of Random Fields

  • K. Breitung
Part of the Solid Mechanics and its Applications book series (SMIA, volume 47)


In many applications random influences are modelled by random fields. Examples can be found in [3] and [11]


Random Field Covariance Function High Order Approximation Gaussian Random Field Conditional Covariance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R.J. Adler. The Geometry of Random Fields. Wiley, New York, 1981.zbMATHGoogle Scholar
  2. 2.
    N. Bleistein and R.A. Handelsman. Asymptotic Expansions of Integrals. Dover Publications Inc., New York, 1986. Reprint of the edition by Holt, Rinehart and Winston, New York, 1975.Google Scholar
  3. 3.
    V.V. Bolotin. Wahrscheinlichkeitsmethoden zur Berechnung von Konstruktionen. VEB-Verlag fur das Bauwesen, Berlin (GDR), 1981Google Scholar
  4. 4.
    K. Breitung. Asymptotic approximations for the extreme value distribution of non- stationary differentiable normal processes. In Transactions of the Tenth Prague Conference on Information Theory, Statistical Decision Functions and Random Processes 1986, volume I, pages 207–215, Prague, Czech. Rep., 1988. AcademiaMathSciNetGoogle Scholar
  5. 5.
    K. Breitung. The extreme value distribution of non-stationary vector processes. In A. H.-S. Ang, M. Shinozuka, and G.I. Schueller, editors, Proceedings of ICOSSAR ´89 5th Int´l Ccnf. on structural safety and reliability, volume II, pages 1327–1332. American Society of Civil Engineers, 1990Google Scholar
  6. 6.
    K. Breitung. Asymptotic Approximations for Probability Integrals. Springer, Berlin, 1994. Lecture Notes in Mathematics, Nr. 1592zbMATHGoogle Scholar
  7. 7.
    M. Knowles and D. Siegmund. On Hotelling´s approach to testing for a nonlinear parameter in regression. International Statistical Review, 57(3):205–220, 1989zbMATHCrossRefGoogle Scholar
  8. 8.
    M.R. Leadbetter, G. Lindgren, and H. Rootzen. Extremes and Related Properties of Random Sequences and Processes. Springer, New York, 1983zbMATHGoogle Scholar
  9. 9.
    A. Papoulis. Probability, Random Variables and Stochastic Processes. McGraw-Hill, New York, third edition, 1991.Google Scholar
  10. 10.
    J. Sun. Tail probabilities of the maxima of Gaussian random fields. The Annals of Probability, 21(1):34–71, 1993MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    D. Veneziano, M. Grigoriu, and C.A. Cornell. Vector process models for system reliability. Journal of the Engineering Mechanics Division ASCE 103(3):441–460, 1977Google Scholar

Copyright information

© Kluwer Academic publishers 1996

Authors and Affiliations

  • K. Breitung
    • 1
  1. 1.Department of Civil EngineeringUniversity of CalgaryCalgaryCanada

Personalised recommendations