{"title":"Power Levy motion. II. Evolution.","authors":"Iddo Eliazar","doi":"10.1063/5.0251341","DOIUrl":null,"url":null,"abstract":"<p><p>This is the second part of a pair of papers that introduce and explore power Levy motion (PLM). The first part constructed PLM and explained its emergence and rationale. Taking on a \"diffusion perspective,\" the first part addressed key facets and features of PLM. Taking on an \"evolution perspective,\" this part continues the investigation of PLM and addresses its following facets and features: Markov dynamics and propagator; simulation; increments' conditional distributions; persistence and anti-persistence; power-law asymptotics and Taylor's law; integral representation; Langevin dynamics and stochastic differential equation; center-reversion and center-repulsion; decreasing and increasing volatility; Lamperti transformation and Ornstein-Uhlenbeck representation. This pair of papers establishes PLM as a potent and compelling anomalous-diffusion model and presents a comprehensive exposition of PLM.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7000,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1063/5.0251341","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This is the second part of a pair of papers that introduce and explore power Levy motion (PLM). The first part constructed PLM and explained its emergence and rationale. Taking on a "diffusion perspective," the first part addressed key facets and features of PLM. Taking on an "evolution perspective," this part continues the investigation of PLM and addresses its following facets and features: Markov dynamics and propagator; simulation; increments' conditional distributions; persistence and anti-persistence; power-law asymptotics and Taylor's law; integral representation; Langevin dynamics and stochastic differential equation; center-reversion and center-repulsion; decreasing and increasing volatility; Lamperti transformation and Ornstein-Uhlenbeck representation. This pair of papers establishes PLM as a potent and compelling anomalous-diffusion model and presents a comprehensive exposition of PLM.
期刊介绍：
Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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