加性脉冲噪声驱动的分数阶调和振子的反常扩散

Anomalous diffusion of fractional harmonic oscillator driven by additive impulsive noise

摘要:

本文研究了加性脉冲噪声驱动的分数阶调和振子的反常扩散. 利用Laplace变换与双Laplace变换方法，本文得到了振子位移的均值、方差、关联函数及均方位移. 然后，基于Mittag-Leffler函数的渐进性质，本文进一步研究了振子的短时及长时扩散行为. 研究表明，加性脉冲噪声能够增强振子的短时超扩散，并增大振子的长时欠扩散均方位移.

Abstract:

Anomalous diffusion of a fractional harmonic oscillator driven by both thermal noise and additive impulsive noise is investigated. By using the Laplace and double Laplace transform techniques, the mean, variance, correlation function and mean square displacement (MSD) of the oscillator are expressed by generalized Mittag-Leffler functions with three parameters. Furthermore, asymptotic diffusive behavior of the oscillator is investigated in terms of the asymptotic properties of generalized Mittag-Leffler function. It is shown that the impulsive noise enhances the ballistic diffusion of the oscillator for short time-lag and adds a constant to the mean square displacement for long time-lag.