Levy噪声下的谐振子：相空间中的意外性质
Harmonic oscillator under Levy noise: Unexpected properties in the phase space
摘要：
受噪声影响的谐振子是各种物理现象的基本模型。在高斯白噪声作用下，振子的位置和速度是独立的随机变量，它们服从椭圆水平线的二元高斯分布。相分布均匀。这些性质在一般的莱维情况下都不成立。因此，联合概率密度的能级线不是椭圆的。振子的坐标和速度是强相关的，这种依赖性通过引入相应的参数（“宽度赤字”）来量化。相位的分布是不均匀的，并且是高度非平凡的。
英文摘要：
A harmonic oscillator under influence of the noise is a basic model of various physical phenomena. Under Gaussian white noise the position and velocity of the oscillator are independent random variables which are distributed according to the bivariate Gaussian distribution with elliptic level lines. The distribution of phase is homogeneous. None of these properties hold in the general Lévy case. Thus, the level lines of the joint probability density are not elliptic. The coordinate and the velocity of the oscillator are strongly dependent, and this dependence is quantified by introducing the corresponding parameter ("width deficit"). The distribution of the phase is inhomogeneous and highly nontrivial.
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