Statistical performance analysis of nonlinear stochastic systems by the Monte Carlo method

Until the recent advent of extended covariance analysis utilizing quasi-linearization techniques, the only approach for assessing the performance of a nonlinear system with random inputs and initial conditions has been the monte carlo method. This method involves direct simulation, i.e., determining the system response to a finite number of “typical” initial conditions and noise input functions which are generated according to their specified statistics, and averaging over the resulting ensemble of responses (“trials”) to obtain estimated or sample statistics.