关联色噪声驱动的线性系统的统计分析

The Statistic Analysis of a Linear System Driven by Correlated Colored Noises

精确计算了关联时间为τ1和τ2的两相关O－U噪声所驱动线性系统的关联函数、功率谱及定态几率分布．发现：a．噪声间关联强度λ对系统的关联函数、功率谱及定态几率分布都有很大的影响；b．当驱动两O－U噪声的白噪声间的关联时间τ和两O－U噪声的自关联时间相等（τ=τ1=τ2）时，直接关联和间接关联所计算出来的关联函数、功率谱及定态几率分布是相同的；C．在完全负关联（λ=－1），且各噪声的关联时间和强度都相等时，系统的关联函数、功率谱及相对涨落变为0，即确定论情形．

The correlation function, power spectrum and the stationary probability distribution of alinear system driven by two correlated O-U noises with correlation time τ1 and τ2 respectively are calculated. It is found that: the correlated strength τ between the noises has significant effect on theabove-mentioned statistic quantities； when the correlation time τ between white noises and the twoself-correlation time of two O-U noises are equal (τ＝τ1＝τ2,), these quantities calculated for directcorrelation or indirect correlation are the same respectively; the correlation function, power spectrumand the relative fluctuation of the system all become zero under complete negative correlation andwhen the correlation time and strength of all noises are equal, it is a case of deterministic correlation.