... a Kolmogorov backward equation . We then show the similarity by adopting conditional expectation as our projection operator in the generalized Langevin equation . The characteristics of the conditional expectation play a central role in our study. 04 10 2007 01 05 2007 stochastic systems...

... methods least squares approximations stochastic systems dynamic systems stochastic response random vibration mean-square response Dynamic systems are often excited by inputs that can be approximated as “white” in frequency content ( 1 ). In other cases, white noise inputs processed...

... stochastic system are estimated under the available information about the moment response of the system. With the estimated entropy and property of entropy stability, a robust stability boundary of the nonlinear stochastic system is predicted. Next, for the prediction of response statistics, a statistical...

...O. Elbeyli; J. Q. Sun This paper presents a method for designing covariance type controls of nonlinear stochastic systems. The method consists of two steps. The first step is to find a class of nonlinear feedback controls with undetermined gains such that the exact stationary PDF of the response...

... that the response based on the Rayleigh approximation is close to that via the simulation for an initial period. This results supports the short time Gaussian approximation (STGA) 25 . 6 7 8 In this paper, a design method of feedback controls of nonlinear stochastic systems has been...