Accuracy analysis of statistical linearization methods applied to nonlinear dynamical systems

摘要

The purpose of this paper is to present the accuracy analysis of statistical linearization methods applied to dynamical systems described by nonlinear integral equations defined over locally compact Abelian groups. Nonstationary dynamical systems are considered as well as stationary ones. The technique of generalized harmonic analysis of noncommutativc causal operators from L~1(G;L(R~n, R~n)) is used to analyse special Banach algebras of integral operators being limiting filters. Bounds on the statistical linearization error between the exact and approximate solutions are given. The existence conditions of the mean-square continuous exact solutions are considered too. To compare presented statistical linearization methods with exact solutions, for different statistical linearization methods, an illustrative example is given.