Stochastic averaging of quasi integrable and non-resonant Hamiltonian systems excited by fractional Gaussian noise With Hurst index H [formula omitted] (1/2,1)

Abstract

A stochastic averaging method of quasi integrable and non-resonant Hamiltonian systems under excitation of fractional Gaussian noise (fGn) with Hurst index 1/2<H <1 is proposed. First, the definitions and the basic properties of fGn and fractional Brownian motion (fBm) are briefly introduced. Then, the averaged fractional stochastic differential equations (SDEs) for the first integrals are derived. The dimension of averaged fractional SDEs is a half of that of the original system. The stationary probability density and statistics of the original system are then obtained approximately from solving the averaged fractional SDEs numerically. Two examples are given to illustrate the proposed stochastic averaging method. It is shown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of original system agree well.