关联白噪声驱动单稳系统的统计性质的研究

Statistical Properties of Mono-state System Driven by Correlated White Noise

我们研究了关联白噪声驱动单稳系统的平均首通时间(MFPT)与概率分布.通过比较解析与数值计算的结果发现它们的变化趋势是一致的.因此我们得到以下结论:(1)在不同的关联强度下,概率分布的稳态的位置不同,在正关联的情况下,稳态左移;(2)当弱关联时平均首通时间随着乘性/加性噪声强度的增大而减小,在强关联下,出现了一个峰值;(3)平均首通时间随着乘性与加性噪声的关联强度增大而增大.

By theoretical approximation and numerical simulations, the mean first passage time （MFPT） and distribution of the probability in a mono - state system driven by cross - correlation between multiplicative and additive noise are investigated. Despite the bad agreement on the absolute value, it is clear that the slope of theoretical approximation is well reproduced by the numerical simulations. It is shown that ： （ 1 ） The distribution of the probability is effected by the correlated strength ; （2） The MFPT decreases with increasing the multiplicative or additive noise intensity; （3） The MFPT increases with increasing the correlated strength.