Stochastic analysis of time-variant nonlinear dynamic systems. Part1: the Fokker-Planck-Kolmogorov Equation approach in stochastic mechanics

摘要

The probabilistic description and analysis of the response of time-invariant nonlinear dynamic systems driven by stochastic processes is usually treated by means of evaluation of statistical moments and cumulants of the response. The background of these methods is the Fokker-Planck-Kolmogorov (FPK) equation for a probability density function or the Pugachev equation for a characteristic function, respectively. The exact solutions of these equations are obtained only for isolated cases.