非高斯噪声源诱导扩散的广义维纳过程和kolmogorov方程

A. Dubkov, Bernardo Spagnol
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引用次数: 31

摘要

我们证明了用于描述非高斯白噪声源的广义维纳过程的增量具有无限可分随机过程的性质。利用泛函方法和新的非高斯白噪声的相关公式,直接从Langevin方程推导出具有这种随机源的马尔可夫非高斯过程的Kolmogorov方程。由该方程得到了高斯白噪声驱动非线性系统的Fokker-Planck方程,不连续马尔可夫过程的Kolmogorov-Feller方程,以及反常扩散的分数阶Fokker-Planck方程。导出了一些简单的异常扩散情况下的平稳概率分布。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
GENERALIZED WIENER PROCESS AND KOLMOGOROV’S EQUATION FOR DIFFUSION INDUCED BY NON-GAUSSIAN NOISE SOURCE
We show that the increments of generalized Wiener process, useful to describe non-Gaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for non-Gaussian white noise we derive directly from Langevin equation, with such a random source, the Kolmogorov's equation for Markovian non-Gaussian process. From this equation we obtain the Fokker–Planck equation for nonlinear system driven by white Gaussian noise, the Kolmogorov–Feller equation for discontinuous Markovian processes, and the fractional Fokker–Planck equation for anomalous diffusion. The stationary probability distributions for some simple cases of anomalous diffusion are derived.
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