Accuracy analysis of statistical linearization methods in nonlinear continuous systems described by random integral equations

The aim of this paper is to present the accuracy analysis of dynamic systems described by nonlinear Volterra integral equations of the second kind. A nonstationary dynamic system is considered as well as a stationary one. The technique of harmonic analysis of noncommutative causal operators from L^1 (R; L(R^n,R^n)) is used to analyse the special Banach algebras of integral operators being limiting filters. A bound of the statistical linearization error between the exact and approximate solutions is given. The conditions under which mean-square continuous exact solutions exist are considered too. To compare presented methods with exact analytical solutions for different statistical linearization methods an illustrative example is given.