非均匀介质中的反常扩散：时间从属非线性朗之万方程产生的信号的功率谱密度
Anomalous diffusion in nonhomogeneous media: Power spectral density of signals generated by time-subordinated nonlinear Langevin equations
摘要：
一维随机系统的次扩散行为可用时间服从的Langevin方程描述。相应的概率密度满足时间分数Fokker-Planck方程。在齐次系统中，由这种Langevin方程产生的信号的功率谱密度具有指数小于1的幂律频率依赖性。本文考虑非齐次系统，证明了在这类系统中，功率谱密度在很宽的中频范围内具有指数等于或大于1的幂律行为。
英文摘要：
Subdiffusive behavior of one-dimensional stochastic systems can be described by time-subordinated Langevin equations. The corresponding probability density satisfies the time-fractional Fokker-Planck equations. In the homogeneous systems the power spectral density of the signals generated by such Langevin equations has power-law dependency on the frequency with the exponent smaller than 1. In this paper we consider nonhomogeneous systems and show that in such systems the power spectral density can have power-law behavior with the exponent equal to or larger than 1 in a wide range of intermediate frequencies.
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