Studies in nonlinear stochastic processes. I. Approximate solutions of nonlinear stochastic differential equations by the method of statistical linearization

A method based on a variational procedure is presented which provides simple and useful approximate solutions to a wide variety of nonlinear stochastic differential equations. This method of statistical linearization is most successful when the stochasticity of the differential equation is due to excitations which are normally distributed or harmonic with random phase. Effects due to deviations from normality can be corrected for in a systematic fashion. Comments regarding existence and uniqueness are given and some error bounds arising from the use of statistical linearization are computed.Supported by the National Science Foundation under Grants NSF GP 32031X and MPS72-04353 A03.