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首页> 外文期刊>Physica, A. Statistical mechanics and its applications >From shape to randomness: A classification of Langevin stochasticity
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From shape to randomness: A classification of Langevin stochasticity

机译：从形状到随机性：Langevin随机性的分类

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摘要

The Langevin equation-perhaps the most elemental stochastic differential equation in the physical sciences-describes the dynamics of a random motion driven simultaneously by a deterministic potential field and by a stochastic white noise. The Langevin equation is, in effect, a mechanism that maps the stochastic white-noise input to a stochastic output: a stationary steady state distribution in the case of potential wells, and a transient extremum distribution in the case of potential gradients. In this paper we explore the degree of randomness of the Langevin equation's stochastic output, and classify it à la Mandelbrot into five states of randomness ranging from "infra-mild" to "ultra-wild". We establish closed-form and highly implementable analytic results that determine the randomness of the Langevin equation's stochastic output-based on the shape of the Langevin equation's potential field.
机译：Langevin方程-也许是物理学中最基本的随机微分方程-描述了由确定性势场和随机白噪声同时驱动的随机运动的动力学。 Langevin方程实际上是一种将随机白噪声输入映射为随机输出的机制：在势阱情况下为稳态稳态分布，在势梯度情况下为瞬态极值分布。在本文中，我们探讨了Langevin方程的随机输出的随机度，并在Mandelbrot上将其分类为从“弱红外”到“超野生”的五个随机状态。我们基于Langevin方程的势场形状，建立了确定Langevin方程的随机输出随机性的封闭形式和高度可实现的分析结果。

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