{"title":"An approximate solution of a perturbed Fokker-Planck equation","authors":"Yan Luo , Kaicheng Sheng","doi":"10.1016/j.jmaa.2025.130040","DOIUrl":null,"url":null,"abstract":"<div><div>This paper focuses on finding an approximate solution of a kind of Fokker-Planck equation with time-dependent perturbations. A formulation of the approximate solution of the equation is constructed, and then the existence of the formulation is proved. The related Hamiltonian dynamical system explains the estimations. Examples of the Ornstein-Uhlenbeck process model and the nonlinear Langevin equation are used to validate the proposed results. Our work provides a more comprehensive understanding of the long-time behaviour of systems described by this Fokker-Planck equation and the corresponding stochastic differential equation.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130040"},"PeriodicalIF":1.2000,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X25008212","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper focuses on finding an approximate solution of a kind of Fokker-Planck equation with time-dependent perturbations. A formulation of the approximate solution of the equation is constructed, and then the existence of the formulation is proved. The related Hamiltonian dynamical system explains the estimations. Examples of the Ornstein-Uhlenbeck process model and the nonlinear Langevin equation are used to validate the proposed results. Our work provides a more comprehensive understanding of the long-time behaviour of systems described by this Fokker-Planck equation and the corresponding stochastic differential equation.
期刊介绍:
The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
Papers are sought which employ one or more of the following areas of classical analysis:
• Analytic number theory
• Functional analysis and operator theory
• Real and harmonic analysis
• Complex analysis
• Numerical analysis
• Applied mathematics
• Partial differential equations
• Dynamical systems
• Control and Optimization
• Probability
• Mathematical biology
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• Mathematical physics.