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Approximate Gaussian representation of evolution equations. I: Single degree of freedom nonlinear equations. (English) Zbl 0588.60053

We have developed a generalization of the method of statistical linearization to enable us to describe transient and other nonstationary phenomena obeying stochastic nonlinear differential equations. This approximation technique provides an optimal Gaussian representation with time-dependent parameters. The algorithm specifies a set of ordinary differential equations for the Gaussian parameters in terms of the time- dependent average nonlinearities. We apply the general formalism developed herein for single degree of freedom dissipative systems to a particular example.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G35 Signal detection and filtering (aspects of stochastic processes)
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