Some observations on the stochastic averaging method

Abstract

Formulas required for the application of Stratonovich's stochastic averaging method are rederived using a mathematical procedure more appealing to engineers. By so doing the physical implications are made clear, allowing certain variations and relaxation of some restrictions. In particular, the time-averaging portion of the original method is removed so that it becomes applicable to non-stationary excitations as well as cases where deterministic time-varying properties must be preserved. A less restrictive general condition is proposed for this modified stochastic averaging method, and heuristic arguments are given for further relaxation of the condition in stability analyses. Application of this modified method is illustrated by a simple example. © 1986.