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Theoretical Error Bounds for Stochastic Linearization of Feedback Systems

Stochastic linearization is a useful method to analyze a class of nonlinear stochastic dynamical systems. An important feature is that it does not require Monte Carlo simulation, which is advantageous especially for dynamics whose extremal outliers are not negligible. However, the resulting accuracy has so far been examined only by numerical experiments, which is usually comparison with Monte Carlo simulation with sufficiently large sample size. In view of this, we derive novel error bounds for stochastic linearization of feedback systems in this paper. The practical usefulness is examined through a numerical example.