Srokowski T
Institute of Nuclear Physics, PL-31-342 Kraków, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Sep;64(3 Pt 1):031102. doi: 10.1103/PhysRevE.64.031102. Epub 2001 Aug 14.
The kangaroo process (KP) is characterized by various forms of covariance and can serve as a useful model of random noises. We discuss properties of that process for the exponential, stretched exponential, and algebraic (power-law) covariances. Then we apply the KP as a model of noise in the generalized Langevin equation and simulate solutions by a Monte Carlo method. Some results appear to be incompatible with requirements of the fluctuation-dissipation theorem because probability distributions change when the process is inserted into the equation. We demonstrate how one can construct a model of noise free of that difficulty. This form of the KP is especially suitable for physical applications.
袋鼠过程（KP）具有多种形式的协方差，可作为随机噪声的有用模型。我们讨论了该过程在指数协方差、拉伸指数协方差和代数（幂律）协方差下的性质。然后，我们将KP用作广义朗之万方程中的噪声模型，并通过蒙特卡罗方法模拟解。一些结果似乎不符合涨落耗散定理的要求，因为当将该过程插入方程时，概率分布会发生变化。我们展示了如何构建一个没有该困难的噪声模型。这种形式的KP特别适合物理应用。
