Approximation of stochastic equilibria for dynamical systems with parametrical noise

Abstract

A problem of the approximation for stochastic equilibria for the system with parametrical noise is considered. Our approach is based on first approximation stochastic systems technique. For these systems, we use a spectral theory of positive operators for the analysis of exponential mean square stability. Using this method we approximate a dispersion of random states in stochastic equilibrium of nonlinear dynamical system with parametrical noise.