Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

Stochastic Linearization: The Theory

Pierre Bernard and Liming Wu
Journal of Applied Probability
Vol. 35, No. 3 (Sep., 1998), pp. 718-730
Stable URL: http://www.jstor.org/stable/3215646
Page Count: 13
  • Read Online (Free)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Stochastic Linearization: The Theory
Preview not available

Abstract

Very little is known about the quantitative behaviour of dynamical systems with random excitation, unless the system is linear. Known techniques imply the resolution of parabolic partial differential equations (Fokker-Planck-Kolmogorov equation), which are degenerate and of high dimension and for which there is no effective known method of resolution. Therefore, users (physicists, mechanical engineers) concerned with such systems have had to design global linearization techniques, known as equivalent statistical linearization (Roberts and Spanos [5]). So far, there has been no rigorous justification of these techniques, with the notable exception of the paper by Frank Kozin [3]. In this contribution, using large deviation principles, several mathematically founded linearization methods are proposed. These principles use relative entropy, or Kullback information, of two probability measures, and Donsker-Varadhan entropy of a Gaussian measure relatively to a Markov kernel. The method of 'true linearization' ([5]) is justified.

Page Thumbnails

  • Thumbnail: Page 
718
    718
  • Thumbnail: Page 
719
    719
  • Thumbnail: Page 
720
    720
  • Thumbnail: Page 
721
    721
  • Thumbnail: Page 
722
    722
  • Thumbnail: Page 
723
    723
  • Thumbnail: Page 
724
    724
  • Thumbnail: Page 
725
    725
  • Thumbnail: Page 
726
    726
  • Thumbnail: Page 
727
    727
  • Thumbnail: Page 
728
    728
  • Thumbnail: Page 
729
    729
  • Thumbnail: Page 
730
    730