Approximate Stationary Density of the Nonlinear Dynamical Systems Excited With White Noise

Abstract

In this paper, obtaining approximate solution of Fokker-Planck-Kolmogorov (FPK) Equation using compactly supported functions has been discussed. With specific choice of such functions as piecewise multivariable polynomials which are supported on ellipsoidal regions, the parameters to be determined can be considerably decreased compared to Multi- Gaussian Closure scheme [1]. An example commonly considered in the literature has been analyzed and the proposed method has been compared with the Multi-Gaussian Closure scheme. The simulation results indicate that the new scheme is quite successful even if the driving noise is not white Gaussian, but has an exponential correlation function with small correlation time.