Stochastic Linearization and Large Deviations

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


Stochastic equivalent linearization is the most popular approximation method for the dynamic of a non-linear system under random excitation. A complete presentation of this method can be found in [4]. Despite the fact it was introduced 40 years ago, the first justification was proposed by F.Kozin [3] in 1987. Another approach was recently introduced by the author in collaboration with L. Wu [2], based on the use of a large deviation principle. The goal of this contribution is to present this approach to the stochastic dynamic engineering public.


Probability Measure Markov Process Relative Entropy Polish Space Empirical Process 
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.
    Alaoui Ismaili M.(1995) PHD thesis, Université Blaise PascalGoogle Scholar
  2. 2.
    Bernard P., Wu L.(1995) Linéarisation d’un oscillateur excité par un bruit blanc: un point de vue entropique, Report of the Laboratoire de Mathématiques Appliquées, Université Biaise PascalGoogle Scholar
  3. 3.
    Kozin F.(1988) The Method of Statistical Linearization for Non-linear Stochastic Vibrations, in Nonlinear Stochastic Dynamic Engineering Systems, F.Ziegler, G.I.Schueller Editors, Springer VerlagGoogle Scholar
  4. 4.
    Roberts J.B., Spanos P.D.(1990) Random Vibration and Statistical Linearization, J.Wiley and Sons.zbMATHGoogle Scholar
  5. 5.
    S.R.S.Varadhan S.R.S.(1984) Large Deviations and Applications, SIAM Publications 46.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • P. Bernard
    • 1
  1. 1.Laboratoire de Mathématiques Appliquées. URA CNRS 1501Université Blaise Pascal - Clermont FerrandAubière CedexFrance

Personalised recommendations