Some thoughts on averaging techniques in stochastic dynamics

Stochastic averaging and quasi-conservative averaging are used essentially to obtain a one-dimensional Markov approximation describing the response of a randomly excited one-degree-of-freedom system. Difficulties arise when the original physical system is more than one degree of freedom with both low and high damping modes, or/and it has a strongly nonlinear stiffness and the stochastic excitation is non-white. The ways in which such difficulties can be overcome are discussed.