Analysis of a Nonlinear First-Order System with a White Noise Input

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Abstract
A general technique for computing the power spectrum of nonlinear systems is presented, and the method is applied to the Brownian motion of a particle with idealized Coulomb damping. In this method the transition probability is obtained by solving the appropriate Fokker‐Planck equation. Then the autocorrelation function is calculated by an appropriate integration, and finally the power spectrum is found by means of the Wiener‐Khintchine relation. Comparison is made with the method of equivalent linearization, which is applicable to a wide class of nonlinear problems.

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