非线性随机微分方程的Tsallis分布和1/f噪声
Tsallis distributions and 1/f noise from nonlinear stochastic differential equations
摘要：
从非广延统计力学的形式主义中出现的概率分布已被应用于各种问题。在本文中，我们统一建模的分布广泛的1/f噪声的模型。我们提出了一类非线性随机微分方程，给出了信号强度的q-指数或q-高斯分布，揭示了功率谱密度的长程相关性和1/f^beta行为。提出了信号强度具有q指数分布和q高斯分布的1/f^beta噪声的超统计框架。
英文摘要：
Probability distributions which emerge from the formalism of nonextensive statistical mechanics have been applied to a variety of problems. In this paper we unite modeling of such distributions with the model of widespread 1/f noise. We propose a class of nonlinear stochastic differential equations giving both the q-exponential or q-Gaussian distributions of signal intensity, revealing long-range correlations and 1/f^beta behavior of the power spectral density. The superstatistical framework to get 1/f^beta noise with q-exponential and q-Gaussian distributions of the signal intensity in is proposed, as well.
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