Brown and Levy Steady-State Motions.

IF 2.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Entropy Pub Date : 2025-06-16 DOI:10.3390/e27060643
Iddo Eliazar
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引用次数: 0

Abstract

This paper introduces and explores a novel class of Brown and Levy steady-state motions. These motions generalize, respectively, the Ornstein-Uhlenbeck process (OUP) and the Levy-driven OUP. As the OUP and the Levy-driven OUP: the motions are Markov; their dynamics are Langevin; and their steady-state distributions are, respectively, Gauss and Levy. As the Levy-driven OUP: the motions can display the Noah effect (heavy-tailed amplitudal fluctuations); and their memory structure is tunable. And, as Gaussian-stationary processes: the motions can display the Joseph effect (long-ranged temporal dependencies); and their correlation structure is tunable. The motions have two parameters: a critical exponent which determines the Noah effect and the memory structure; and a clock function which determines the Joseph effect and the correlation structure. The novel class is a compelling stochastic model due to the following combination of facts: on the one hand the motions are tractable and amenable to analysis and use; on the other hand the model is versatile and the motions display a host of both regular and anomalous features.

布朗和利维稳态运动。
本文介绍并探讨了一类新的布朗和列维稳态运动。这些运动分别概括了Ornstein-Uhlenbeck过程(OUP)和levy驱动的OUP。作为OUP和levy驱动的OUP,运动是马尔可夫的;它们的动力学是朗之万;它们的稳态分布分别为高斯和利维。作为levy驱动的OUP,运动表现出Noah效应(重尾振幅波动);它们的记忆结构是可调节的。并且,作为高斯平稳过程,运动表现出约瑟夫效应(长时间依赖关系);它们的相关结构是可调的。运动有两个参数:决定诺亚效应和记忆结构的临界指数;以及决定约瑟夫效应和相关结构的时钟函数。由于以下事实的组合,新类是一个引人注目的随机模型:一方面,运动是可处理的,易于分析和使用;另一方面,该模型是通用的,运动显示了许多规则和异常的特征。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Entropy
Entropy PHYSICS, MULTIDISCIPLINARY-
CiteScore
4.90
自引率
11.10%
发文量
1580
审稿时长
21.05 days
期刊介绍: Entropy (ISSN 1099-4300), an international and interdisciplinary journal of entropy and information studies, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish as much as possible their theoretical and experimental details. There is no restriction on the length of the papers. If there are computation and the experiment, the details must be provided so that the results can be reproduced.
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