Dichotomous-noise-driven oscillators

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Abstract
The problem of finding the probability density function of the output of an oscillator (a filter of order higher than the first) driven by dichotomous Markov noise (the random telegraph signal) is considered. No known theoretical methods are available for completely solving problems of this type. A somewhat general expression is derived for the output moments and an exact formulation for the probability density is presented in terms of Fokker-Planck–type equations. However, partly because of irregularly shaped boundaries, the Fokker-Planck equations are complicated and remain unsolved except in the first-order case. The paper concludes with some Monte Carlo results for a second-order Butterworth filter.

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