STOCHASTIC LINEARIZATION - THE THEORY

Very little is known about the quantitative behaviour of dynamical sys tems with random excitation, unless the system is linear. Known techni ques 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 resoluti on. Therefore, users (physicists, mechanical engineers) concerned with such systems have had to design global linearization techniques, know n as equivalent statistical linearization (Roberts and Spanos [5]). So far, there has been no rigorous justification of these techniques, wi th the notable exception of the paper by Frank Kozin [3]. In this cont ribution, using large deviation principles, several mathematically fou nded linearization methods are proposed. These principles use relative entropy, or Kullback information, of two probability measures, and Do nsker-Varadhan entropy of a Gaussian measure relatively to a Markov ke rnel. The method of 'true linearization' ([5]) is justified.