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Stochastic Linearization: The Theory
Pierre Bernard and Liming Wu
Journal of Applied Probability
Vol. 35, No. 3 (Sep., 1998), pp. 718-730
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3215646
Page Count: 13
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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 ). So far, there has been no rigorous justification of these techniques, with the notable exception of the paper by Frank Kozin . 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' () is justified.
Journal of Applied Probability © 1998 Applied Probability Trust