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首页> 外文期刊>International journal of non-linear mechanics >Stochastic averaging of quasi integrable and non-resonant Hamiltonian systems excited by fractional Gaussian noise With Hurst index H ∈ (1/2,1)
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Stochastic averaging of quasi integrable and non-resonant Hamiltonian systems excited by fractional Gaussian noise With Hurst index H ∈ (1/2,1)

机译：分数可斯和非共振哈密顿系统的随机平均，其分数为高斯噪声，Hurst指数为H∈（1 / 2,1）

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摘要

A stochastic averaging method of quasi integrable and non-resonant Hamiltonian systems under excitation of fractional Gaussian noise (fGn) with Hurst index 1/2H1 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. (C) 2017 Elsevier Ltd. All rights reserved.
机译：提出了一种在Hurst指数为1/2

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